{"code":0,"msg":"success","data":[[{"head_title":"解答题","questions":[{"question_id":"2062484","question_type":"5","question_channel_type":"6","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"2","evaluated":"0","region_ids":"","grade_id":"8","question_source":"","mode":"2","title":"如图,一次函数y=x+1的图象与反比例函数y=kx(k为常数,且k≠0)的图象都经过点A(m,2).(1)求点A的坐标及反比例函数的表达式;(2)设...","kid_num":"1","paperid":"0","save_num":"151","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"
如图,一次函数y=x+1的图象与反比例函数y=(k为常数,且k≠0)的图象都经过点A(m,2).
(1)求点A的坐标及反比例函数的表达式;
(2)设一次函数y=x+1的图象与x轴交于点B,若点P是x轴上一点,且满足△ABP的面积是2,直接写出点P的坐标.
","options":"","sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"5"},"sort":1,"sort2":1,"is_use":0},{"question_id":"2062259","question_type":"5","question_channel_type":"6","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"2","evaluated":"0","region_ids":"","grade_id":"8","question_source":"","mode":"2","title":"如图,在平面直角坐标系中,一次函数y=ax+b的图象与反比例函数y=kx的图象交于一、三象限内的A、B两点,与x轴交于C点,点A的坐标为(2,m)...","kid_num":"1","paperid":"0","save_num":"190","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"如图,在平面直角坐标系中,一次函数y=ax+b的图象与反比例函数y=的图象交于一、三象限内的A、B两点,与x轴交于C点,点A的坐标为(2,m),点B的坐标为(n,﹣2),tan∠BOC= .
(1)求该反比例函数和一次函数的解析式.
(2)求△BOC的面积.
(3)P是x轴上的点,且△PAC的面积与△BOC的面积相等,求P点的坐标.
","options":"","sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"5"},"sort":2,"sort2":2,"is_use":0},{"question_id":"2563488","question_type":"5","question_channel_type":"6","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"2","evaluated":"0","region_ids":"","grade_id":"9","question_source":"","mode":"2","title":"如图,直线y=x+1与y轴交于A点,与反比例函数y=kx(x>0)的图象交于点M,过M作MH⊥x轴于点H,且tan∠AHO=12.(1)求k的值;(2)设点N(1...","kid_num":"1","paperid":"0","save_num":"158","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"如图,直线y=x+1与y轴交于A点,与反比例函数y=(x>0)的图象交于点M,过M作MH⊥x轴于点H,且tan∠AHO= .
(1)求k的值;
(2)设点N(1,a)是反比例函数y=(x>0)图象上的点,在y轴上是否存在点P,使得PM+PN最小?若存在,求出点P的坐标;若不存在,请说明理由.
","options":"","sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"5"},"sort":3,"sort2":3,"is_use":0}],"scores":{"2062259":{"score":"5"},"2062484":{"score":"5"},"2563488":{"score":"5"}},"sum_score":15,"question_num":3},{"head_title":"综合题","questions":[{"question_id":"2728981","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"24","grade_id":"9","question_source":"2016年贵州省安顺市中考数学试卷","mode":"2","title":"(2016•安顺)如图,在平面直角坐标系中,一次函数y=kx+b(k≠0)的图象与反比例函数y= (m≠0)的图象交于A、B两点,与x轴交于C点,点A的坐标为(n,6),点C的坐标为(﹣2,0),且tan∠ACO=2.
\n\n","kid_num":"1","paperid":"44175","save_num":"42","oldqid":"0","explain_sort_need":"0","paper":{"pid":"44175","title":"2016年贵州省安顺市中考数学试卷"},"extra_file":"","question_text":"如图,在平面直角坐标系中,一次函数y=kx+b(k≠0)的图象与反比例函数y= (m≠0)的图象交于A、B两点,与x轴交于C点,点A的坐标为(n,6),点C的坐标为(﹣2,0),且tan∠ACO=2. ","options":"","sub_explanation":null,"list":[{"question_id":"38957912","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-08-15 06:20:03","update_by":"","update_uid":"0","update_date":"2024-01-26 06:38:49","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2728981","sort":4,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求该反比例函数和一次函数的解析式;","options":"","answer":"解:过点A作AD⊥x轴,垂足为D
由A(n,6),C(﹣2,0)可得,
OD=n,AD=6,CO=2
∵tan∠ACO=2
∴ =2,即 =2
∴n=1
∴A(1,6)
将A(1,6)代入反比例函数,得m=1×6=6
∴反比例函数的解析式为
将A(1,6),C(﹣2,0)代入一次函数y=kx+b,可得
解得
∴一次函数的解析式为y=2x+4
","answer_json":["解:过点A作AD⊥x轴,垂足为D由A(n,6),C(﹣2,0)可得,
OD=n,AD=6,CO=2
∵tan∠ACO=2
∴ =2,即 =2
∴n=1
∴A(1,6)
将A(1,6)代入反比例函数,得m=1×6=6
∴反比例函数的解析式为
将A(1,6),C(﹣2,0)代入一次函数y=kx+b,可得
解得
∴一次函数的解析式为y=2x+4
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"38957914","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-08-15 06:20:03","update_by":"","update_uid":"0","update_date":"2024-01-26 06:38:49","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2728981","sort":5,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求点B的坐标.","options":"","answer":"解:由 可得解得x1=1,x2=﹣3
∵当x=﹣3时,y=﹣2
∴点B坐标为(﹣3,﹣2)
","answer_json":["解:由 可得解得x1=1,x2=﹣3
∵当x=﹣3时,y=﹣2
∴点B坐标为(﹣3,﹣2)
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"10","subScore":["5","5"]},"sort":4,"sort2":4,"is_use":0},{"question_id":"2683292","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"23","grade_id":"9","question_source":"2016年四川省泸州市中考数学试卷","mode":"2","title":"(2016•泸州)如图,一次函数y=kx+b(k<0)与反比例函数y= mx 的图象相交于A、B两点,一次函数的图象与y轴相交于点C,已知点A(4,1) ","kid_num":"1","paperid":"40783","save_num":"55","oldqid":"0","explain_sort_need":"0","paper":{"pid":"40783","title":"2016年四川省泸州市中考数学试卷"},"extra_file":"","question_text":"如图,一次函数y=kx+b(k<0)与反比例函数y= 的图象相交于A、B两点,一次函数的图象与y轴相交于点C,已知点A(4,1)
","options":"","sub_explanation":null,"list":[{"question_id":"38970536","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-07-22 11:09:20","update_by":"","update_uid":"0","update_date":"2024-01-26 07:08:41","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2683292","sort":6,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求反比例函数的解析式;","options":"","answer":"解:∵点A(4,1)在反比例函数y= 的图象上,∴m=4×1=4,
∴反比例函数的解析式为y= .
解:∵点A(4,1)在反比例函数y= 的图象上,
∴m=4×1=4,
∴反比例函数的解析式为y= .
∴设点B的坐标为(n, ).
将y=kx+b代入y= 中,得:
kx+b= ,整理得:kx2+bx﹣4=0,
∴4n=﹣ ,即nk=﹣1①.
令y=kx+b中x=0,则y=b,
即点C的坐标为(0,b),
∴S△BOC= bn=3,
∴bn=6②.
∵点A(4,1)在一次函数y=kx+b的图象上,
∴1=4k+b③.
联立①②③成方程组,即 ,
解得: ,
∴该一次函数的解析式为y=﹣ x+3.
解:∵点B在反比例函数y= 的图象上,
∴设点B的坐标为(n, ).
将y=kx+b代入y= 中,得:
kx+b= ,整理得:kx2+bx﹣4=0,
∴4n=﹣ ,即nk=﹣1①.
令y=kx+b中x=0,则y=b,
即点C的坐标为(0,b),
∴S△BOC= bn=3,
∴bn=6②.
∵点A(4,1)在一次函数y=kx+b的图象上,
∴1=4k+b③.
联立①②③成方程组,即 ,
解得: ,
∴该一次函数的解析式为y=﹣ x+3.
如图,直线y= x+2与双曲线相交于点A(m,3),与x轴交于点C.
","options":"","sub_explanation":null,"list":[{"question_id":"38999238","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-07-01 04:00:25","update_by":"","update_uid":"0","update_date":"2024-01-26 08:27:06","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2575329","sort":8,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求双曲线解析式;","options":"","answer":"解:把A(m,3)代入直线解析式得:3= m+2,即m=2,∴A(2,3),
把A坐标代入y= ,得k=6,
则双曲线解析式为y=
","answer_json":["解:把A(m,3)代入直线解析式得:3= m+2,即m=2,
∴A(2,3),
把A坐标代入y= ,得k=6,
则双曲线解析式为y=
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"38999240","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-07-01 04:00:25","update_by":"","update_uid":"0","update_date":"2024-01-26 08:27:06","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2575329","sort":9,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"点P在x轴上,如果△ACP的面积为3,求点P的坐标.","options":"","answer":"解:对于直线y= x+2,令y=0,得到x=﹣4,即C(﹣4,0),设P(x,0),可得PC=|x+4|,
∵△ACP面积为3,
∴ |x+4|•3=3,即|x+4|=2,
解得:x=﹣2或x=﹣6,
则P坐标为(﹣2,0)或(﹣6,0).
","answer_json":["解:对于直线y= x+2,令y=0,得到x=﹣4,即C(﹣4,0),
设P(x,0),可得PC=|x+4|,
∵△ACP面积为3,
∴ |x+4|•3=3,即|x+4|=2,
解得:x=﹣2或x=﹣6,
则P坐标为(﹣2,0)或(﹣6,0).
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"10","subScore":["5","5"]},"sort":8,"sort2":6,"is_use":0},{"question_id":"2683612","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"23","grade_id":"9","question_source":"2016年四川省攀枝花市中考数学试卷","mode":"2","title":"(2016•攀枝花)如图,在平面直角坐标系中,O为坐标原点,△ABO的边AB垂直与x轴,垂足为点B,反比例函数y= kx (x>0)的图象经过AO的中...","kid_num":"2","paperid":"40790","save_num":"58","oldqid":"0","explain_sort_need":"0","paper":{"pid":"40790","title":"2016年四川省攀枝花市中考数学试卷"},"extra_file":"","question_text":"如图,在平面直角坐标系中,O为坐标原点,△ABO的边AB垂直与x轴,垂足为点B,反比例函数y= (x>0)的图象经过AO的中点C,且与AB相交于点D,OB=4,AD=3,
∵点C为线段AO的中点,
∴点C的坐标为(2, ).
∵点C、点D均在反比例函数y= 的函数图象上,
∴ ,解得: .
∴反比例函数的解析式为y=
","answer_json":["解:设点D的坐标为(4,m)(m>0),则点A的坐标为(4,3+m),
∵点C为线段AO的中点,
∴点C的坐标为(2, ).
∵点C、点D均在反比例函数y= 的函数图象上,
∴ ,解得: .
∴反比例函数的解析式为y=
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"38970744","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-07-22 11:19:46","update_by":"","update_uid":"0","update_date":"2024-01-26 07:08:57","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2683612","sort":11,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求cos∠OAB的值;","options":"","answer":"解:∵m=1,∴点A的坐标为(4,4),
∴OB=4,AB=4.
在Rt△ABO中,OB=4,AB=4,∠ABO=90°,
∴OA= =4 ,cos∠OAB= =
","answer_json":["解:∵m=1,
∴点A的坐标为(4,4),
∴OB=4,AB=4.
在Rt△ABO中,OB=4,AB=4,∠ABO=90°,
∴OA= =4 ,cos∠OAB= =
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2},{"question_id":"38970746","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-07-22 11:19:46","update_by":"","update_uid":"0","update_date":"2024-01-26 07:08:57","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2683612","sort":12,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求经过C、D两点的一次函数解析式.","options":"","answer":"解:∵m=1,∴点C的坐标为(2,2),点D的坐标为(4,1).
设经过点C、D的一次函数的解析式为y=ax+b,
则有 ,解得: .
∴经过C、D两点的一次函数解析式为y=﹣ x+3
","answer_json":["解:∵m=1,
∴点C的坐标为(2,2),点D的坐标为(4,1).
设经过点C、D的一次函数的解析式为y=ax+b,
则有 ,解得: .
∴经过C、D两点的一次函数解析式为y=﹣ x+3
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":3}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"15","subScore":["5","5","5"]},"sort":10,"sort2":7,"is_use":0},{"question_id":"2575501","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"22","grade_id":"9","question_source":"2016年重庆市中考数学试卷(A卷)","mode":"2","title":"(2016•重庆)在平面直角坐标系中,一次函数y=ax+b(a≠0)的图形与反比例函数y= kx (k≠0)的图象交于第二、四象限内的A、B两点,与y...","kid_num":"1","paperid":"37773","save_num":"46","oldqid":"0","explain_sort_need":"0","paper":{"pid":"37773","title":"2016年重庆市中考数学试卷(A卷)"},"extra_file":"","question_text":"在平面直角坐标系中,一次函数y=ax+b(a≠0)的图形与反比例函数y= (k≠0)的图象交于第二、四象限内的A、B两点,与y轴交于C点,过点A作AH⊥y轴,垂足为H,OH=3,tan∠AOH= ,点B的坐标为(m,﹣2).
AH=4.即A(﹣4,3).
由勾股定理,得
AO= =5,
△AHO的周长=AO+AH+OH=3+4+5=12
","answer_json":["解:由OH=3,tan∠AOH= ,得
AH=4.即A(﹣4,3).
由勾股定理,得
AO= =5,
△AHO的周长=AO+AH+OH=3+4+5=12
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"38999316","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-07-01 04:10:30","update_by":"","update_uid":"0","update_date":"2024-01-26 08:27:38","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2575501","sort":14,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求该反比例函数和一次函数的解析式.","options":"","answer":"解:将A点坐标代入y= (k≠0),得k=﹣4×3=﹣12,
反比例函数的解析式为y= ;
当y=﹣2时,﹣2= ,解得x=6,即B(6,﹣2).
将A、B点坐标代入y=ax+b,得
,
解得 ,
一次函数的解析式为y=﹣ x+1.
","answer_json":["解:将A点坐标代入y= (k≠0),得
k=﹣4×3=﹣12,
反比例函数的解析式为y= ;
当y=﹣2时,﹣2= ,解得x=6,即B(6,﹣2).
将A、B点坐标代入y=ax+b,得
,
解得 ,
一次函数的解析式为y=﹣ x+1.
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"10","subScore":["5","5"]},"sort":13,"sort2":8,"is_use":0},{"question_id":"2536152","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"15","grade_id":"9","question_source":"2016年山东省菏泽市中考数学试卷","mode":"2","title":"(2016•菏泽)如图,在平面直角坐标系xOy中,双曲线y= πx 与直线y=﹣2x+2交于点A(﹣1,a). ","kid_num":"1","paperid":"36178","save_num":"70","oldqid":"0","explain_sort_need":"0","paper":{"pid":"36178","title":"2016年山东省菏泽市中考数学试卷"},"extra_file":"","question_text":"如图,在平面直角坐标系xOy中,双曲线y= 与直线y=﹣2x+2交于点A(﹣1,a).
∴a=﹣2×(﹣1)+2=4,
∴点A的坐标是(﹣1,4),代入反比例函数y= ,
∴m=﹣4.
解:∵点A的坐标是(﹣1,a),在直线y=﹣2x+2上,
∴a=﹣2×(﹣1)+2=4,
∴点A的坐标是(﹣1,4),代入反比例函数y= ,
∴m=﹣4.
∴该双曲线与直线y=﹣2x+2另一个交点B的坐标为(2,﹣2)
","answer_json":["解:解方程组 解得: 或 ,∴该双曲线与直线y=﹣2x+2另一个交点B的坐标为(2,﹣2)
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"10","subScore":["5","5"]},"sort":15,"sort2":9,"is_use":0},{"question_id":"2784114","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"15","grade_id":"9","question_source":"2016年山东省东营市中考数学试卷","mode":"2","title":"(2016•东营)如图,在平面直角坐标系中,直线AB与x轴交于点B,与y轴交于点A,与反比例函数y= mx 的图象在第二象限交于点C,CE⊥x轴,垂...","kid_num":"3","paperid":"47388","save_num":"68","oldqid":"0","explain_sort_need":"0","paper":{"pid":"47388","title":"2016年山东省东营市中考数学试卷"},"extra_file":"","question_text":"如图,在平面直角坐标系中,直线AB与x轴交于点B,与y轴交于点A,与反比例函数y= 的图象在第二象限交于点C,CE⊥x轴,垂足为点E,tan∠ABO= ,OB=4,OE=2.
","options":"","sub_explanation":null,"list":[{"question_id":"38927966","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"21王芳惠","create_uid":"7189882","create_date":"2016-09-08 03:08:30","update_by":"","update_uid":"0","update_date":"2024-01-26 06:09:11","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2784114","sort":17,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求反比例函数的解析式;","options":"","answer":"解:∵OB=4,OE=2,∴BE=OB+OE=6.
∵CE⊥x轴,
∴∠CEB=90°.
在Rt△BEC中,∠CEB=90°,BE=6,tan∠ABO= ,
∴CE=BE•tan∠ABO=6× =3,
结合函数图象可知点C的坐标为(﹣2,3).
∵点C在反比例函数y= 的图象上,
∴m=﹣2×3=﹣6,
∴反比例函数的解析式为y=﹣ .
","answer_json":["解:∵OB=4,OE=2,
∴BE=OB+OE=6.
∵CE⊥x轴,
∴∠CEB=90°.
在Rt△BEC中,∠CEB=90°,BE=6,tan∠ABO= ,
∴CE=BE•tan∠ABO=6× =3,
结合函数图象可知点C的坐标为(﹣2,3).
∵点C在反比例函数y= 的图象上,
∴m=﹣2×3=﹣6,
∴反比例函数的解析式为y=﹣ .
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"38927968","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"21王芳惠","create_uid":"7189882","create_date":"2016-09-08 03:08:30","update_by":"","update_uid":"0","update_date":"2024-01-26 06:09:11","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2784114","sort":18,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"若点D是反比例函数图象在第四象限上的点,过点D作DF⊥y轴,垂足为点F,连接OD、BF.如果S△BAF=4S△DFO , 求点D的坐标.","options":"","answer":"解:∵点D在反比例函数y=﹣ 第四象限的图象上,
∴设点D的坐标为(n,﹣ )(n>0).
在Rt△AOB中,∠AOB=90°,OB=4,tan∠ABO= ,
∴OA=OB•tan∠ABO=4× =2.
∵S△BAF= AF•OB= (OA+OF)•OB= (2+ )×4=4+ .
∵点D在反比例函数y=﹣ 第四象限的图象上,
∴S△DFO= ×|﹣6|=3.
∵S△BAF=4S△DFO ,
∴4+ =4×3,
解得:n= ,
经验证,n= 是分式方程4+ =4×3的解,
∴点D的坐标为( ,﹣4).
","answer_json":["解:∵点D在反比例函数y=﹣ 第四象限的图象上,
∴设点D的坐标为(n,﹣ )(n>0).
在Rt△AOB中,∠AOB=90°,OB=4,tan∠ABO= ,
∴OA=OB•tan∠ABO=4× =2.
∵S△BAF= AF•OB= (OA+OF)•OB= (2+ )×4=4+ .
∵点D在反比例函数y=﹣ 第四象限的图象上,
∴S△DFO= ×|﹣6|=3.
∵S△BAF=4S△DFO,
∴4+ =4×3,
解得:n= ,
经验证,n= 是分式方程4+ =4×3的解,
∴点D的坐标为( ,﹣4).
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"10","subScore":["5","5"]},"sort":17,"sort2":10,"is_use":0},{"question_id":"2683806","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"23","grade_id":"9","question_source":"2016年四川省宜宾市中考数学试卷","mode":"2","title":"(2016•宜宾)如图,一次函数y=kx+b的图象与反比例函数y= mx (x>0)的图象交于A(2,﹣1),B( 12 ,n)两点,直线y=2与y轴交于点C. ","kid_num":"1","paperid":"40796","save_num":"38","oldqid":"0","explain_sort_need":"0","paper":{"pid":"40796","title":"2016年四川省宜宾市中考数学试卷"},"extra_file":"","question_text":"如图,一次函数y=kx+b的图象与反比例函数y= (x>0)的图象交于A(2,﹣1),B( ,n)两点,直线y=2与y轴交于点C.
","options":"","sub_explanation":null,"list":[{"question_id":"38970792","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"1987lee","create_uid":"6286416","create_date":"2016-07-22 11:27:59","update_by":"","update_uid":"0","update_date":"2024-01-26 07:09:09","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"2683806","sort":19,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求一次函数与反比例函数的解析式;","options":"","answer":"解:把A(2,﹣1)代入反比例解析式得:﹣1= ,即m=﹣2,∴反比例解析式为y=﹣ ,
把B( ,n)代入反比例解析式得:n=﹣4,即B( ,﹣4),
把A与B坐标代入y=kx+b中得: ,
解得:k=2,b=﹣5,
则一次函数解析式为y=2x﹣5.
解:把A(2,﹣1)代入反比例解析式得:﹣1= ,即m=﹣2,
∴反比例解析式为y=﹣ ,
把B( ,n)代入反比例解析式得:n=﹣4,即B( ,﹣4),
把A与B坐标代入y=kx+b中得: ,
解得:k=2,b=﹣5,
则一次函数解析式为y=2x﹣5.
∴AB= = ,原点(0,0)到直线y=2x﹣5的距离d= = ,
则S△ABC= AB•d= .
解:∵A(2,﹣1),B( ,﹣4),直线AB解析式为y=2x﹣5,
∴AB= = ,原点(0,0)到直线y=2x﹣5的距离d= = ,
则S△ABC= AB•d= .
如图,在平面直角坐标系中A点的坐标为(8,y),AB⊥x轴于点B,sin∠OAB= , 反比例函数y=的图象的一支经过AO的中点C,且与AB交于点D.
","options":"","sub_explanation":null,"list":[{"question_id":"35130950","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"Tracy0501","create_uid":"6073243","create_date":"2016-01-19 19:46:37","update_by":"","update_uid":"0","update_date":"2024-01-26 16:31:29","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"1553288","sort":21,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求反比例函数解析式","options":"","answer":"解:∵A点的坐标为(8,y),∴OB=8,
∵AB⊥x轴于点B,sin∠OAB= ,
∴= ,
∴OA=10,
由勾股定理得:AB==6,
∵点C是OA的中点,且在第一象限内,
∴C(4,3),
∵点C在反比例函数y=的图象上,
∴k=12,
∴反比例函数解析式为:y=;
","answer_json":["解:∵A点的坐标为(8,y),
∴OB=8,
∵AB⊥x轴于点B,sin∠OAB=,
∴=,
∴OA=10,
由勾股定理得:AB==6,
∵点C是OA的中点,且在第一象限内,
∴C(4,3),
∵点C在反比例函数y=的图象上,
∴k=12,
∴反比例函数解析式为:y=;
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"35131318","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"Tracy0501","create_uid":"6073243","create_date":"2016-01-19 19:46:37","update_by":"","update_uid":"0","update_date":"2024-01-26 16:31:29","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"1553288","sort":22,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"若函数y=3x与y=的图象的另一支交于点M,求三角形OMB与四边形OCDB的面积的比","options":"","answer":"解:将y=3x与y=联立成方程组,得:
,
解得: , ,
∵M是直线与双曲线另一支的交点,
∴M(﹣2,﹣6),
∵点D在AB上,
∴点D的横坐标为8,
∵点D在反比例函数y=的图象上,
∴点D的纵坐标为 ,
∴D(8,),
∴BD= ,
连接BC,如图所示,
∵S△MOB=•8•|﹣6|=24,
S四边形OCDB=S△OBC+S△BCD=•8•3+••4=15,
∴ .
","answer_json":["解:将y=3x与y=联立成方程组,得:
,
解得:,,
∵M是直线与双曲线另一支的交点,
∴M(﹣2,﹣6),
∵点D在AB上,
∴点D的横坐标为8,
∵点D在反比例函数y=的图象上,
∴点D的纵坐标为,
∴D(8,),
∴BD=,
连接BC,如图所示,
∵S△MOB=•8•|﹣6|=24,
S四边形OCDB=S△OBC+S△BCD=•8•3+••4=15,
∴.
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"10","subScore":["5","5"]},"sort":21,"sort2":12,"is_use":0},{"question_id":"1586768","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"","grade_id":"9","question_source":"","mode":"2","title":"(2015•泸州)如图,一次函数y=kx+b(k<0)的图象经过点C(3,0),且与两坐标轴围成的三角形的面积为3.","kid_num":"1","paperid":"0","save_num":"35","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"如图,一次函数y=kx+b(k<0)的图象经过点C(3,0),且与两坐标轴围成的三角形的面积为3.
","options":"","sub_explanation":null,"list":[{"question_id":"35118114","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"三不_GN","create_uid":"6809360","create_date":"2016-01-27 23:01:01","update_by":"","update_uid":"0","update_date":"2024-01-26 16:13:51","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"1586768","sort":23,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求该一次函数的解析式;","options":"","answer":"解:∵一次函数y=kx+b(k<0)的图象经过点C(3,0),∴3k+b=0①,点C到y轴的距离是3,∵k<0,∴b>0,∵一次函数y=kx+b的图象与y轴的交点是(0,b),∴×3×b=3,解得:b=2.把b=2代入①,解得:k= , 则函数的解析式是y=x+2.
故这个函数的解析式为y=x+2;
","answer_json":["解:∵一次函数y=kx+b(k<0)的图象经过点C(3,0),∴3k+b=0①,点C到y轴的距离是3,∵k<0,∴b>0,∵一次函数y=kx+b的图象与y轴的交点是(0,b),∴×3×b=3,解得:b=2.把b=2代入①,解得:k=,则函数的解析式是y=x+2.
故这个函数的解析式为y=x+2;
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"35118116","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"三不_GN","create_uid":"6809360","create_date":"2016-01-27 23:01:01","update_by":"","update_uid":"0","update_date":"2024-01-26 16:13:51","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"1586768","sort":24,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"若反比例函数y=的图象与该一次函数的图象交于二、四象限内的A、B两点,且AC=2BC,求m的值.∵直线AB的解析式为y=x+2,
∴A(3﹣3n,2n),B(3+n,﹣n),∵反比例函数y=的图象经过A、B两点,
∴(3﹣3n)•2n=(3+n)•(﹣n),解得n1=2,n2=0(不合题意舍去),∴m=(3﹣3n)•2n=﹣3×4=﹣12.","answer_json":["解:如图,作AD⊥x轴于点D,BE⊥x轴于点E,则AD∥BE.∵AD∥BE,∴△ACD∽△BCE,∴=2,∴AD=2BE.设B点纵坐标为﹣n,则A点纵坐标为2n.∵直线AB的解析式为y=x+2,
∴A(3﹣3n,2n),B(3+n,﹣n),∵反比例函数y=的图象经过A、B两点,
∴(3﹣3n)•2n=(3+n)•(﹣n),解得n1=2,n2=0(不合题意舍去),∴m=(3﹣3n)•2n=﹣3×4=﹣12."],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":2}],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"10","subScore":["5","5"]},"sort":23,"sort2":13,"is_use":0},{"question_id":"1590607","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"","grade_id":"9","question_source":"内蒙古通辽市开鲁县2019-2020学年九年级下学期数学第二次月考试卷","mode":"2","title":"(2015•乐山)如图,正比例函数y=2x的图象与反比例函数y=kx的图象交于A、B两点,过点A作AC垂直x轴于点C,连结BC.若△ABC的面积为2.","kid_num":"1","paperid":"2672095","save_num":"37","oldqid":"0","explain_sort_need":"0","paper":{"pid":"2672095","title":"内蒙古通辽市开鲁县2019-2020学年九年级下学期数学第二次月考试卷"},"extra_file":"","question_text":"如图,正比例函数y=2x的图象与反比例函数y=\n 的图象交于A、B两点,过点A作AC垂直x轴于点C,连结BC.若△ABC的面积为2.
\n","options":"","sub_explanation":null,"list":[{"question_id":"35116644","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"三不_GN","create_uid":"6809360","create_date":"2016-01-28 18:25:01","update_by":"","update_uid":"0","update_date":"2024-01-26 16:11:40","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"1590607","sort":25,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求k的值;","options":"","answer":"解:∵反比例函数与正比例函数的图象相交于A、B两点,∴A、B两点关于原点对称,
∴OA=OB,
∴△BOC的面积=△AOC的面积=2÷2=1,
又∵A是反比例函数y=图象上的点,且AC⊥x轴于点C,
∴△AOC的面积=|k|,
∴|k|=1,
∵k>0,
∴k=2.
故这个反比例函数的解析式为y=;
","answer_json":["解:∵反比例函数与正比例函数的图象相交于A、B两点,
∴A、B两点关于原点对称,
∴OA=OB,
∴△BOC的面积=△AOC的面积=2÷2=1,
又∵A是反比例函数y=图象上的点,且AC⊥x轴于点C,
∴△AOC的面积=|k|,
∴|k|=1,
∵k>0,
∴k=2.
故这个反比例函数的解析式为y=;
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"35116688","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"三不_GN","create_uid":"6809360","create_date":"2016-01-28 18:25:01","update_by":"","update_uid":"0","update_date":"2024-01-26 16:11:40","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"1590607","sort":26,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"x轴上是否存在一点D , 使△ABD为直角三角形?若存在,求出点D的坐标;若不存在,请说明理由.","options":"","answer":"x轴上存在一点D,使△ABD为直角三角形.将y=2x与y=联立方程组得: , 解得 ,如图,反比例函数(k>0)与正比例函数y=ax相交于A(1,k),B(﹣k,﹣1)两点.
","options":"","sub_explanation":null,"list":[{"question_id":"35126012","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"三不_GN","create_uid":"6809360","create_date":"2016-01-22 17:14:28","update_by":"","update_uid":"0","update_date":"2024-01-26 16:27:23","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"1566293","sort":27,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"求反比例函数和正比例函数的解析式;","options":"","answer":"解:据题意得:点A(1,k)与点B(﹣k,﹣1)关于原点对称,∴k=1,
∴A(1,1),B(﹣1,﹣1),
∴反比例函数和正比例函数的解析式分别为 , y=x;
解:据题意得:点A(1,k)与点B(﹣k,﹣1)关于原点对称,
∴k=1,
∴A(1,1),B(﹣1,﹣1),
∴反比例函数和正比例函数的解析式分别为,y=x;
∴ ,
②﹣①得,y2﹣y1=x2﹣x1 ,
∵|x1﹣x2|•|y1﹣y2|=5,
∴|x1﹣x2|=|y1﹣y2|= ,
由得x2+bx﹣1=0,
解得,x1= , x2= ,
∴|x1﹣x2|=|﹣|=||= ,
解得b=±1.
","answer_json":["解:∵一次函数y=x+b的图象过点(x1,y1)、(x2,y2),
∴,
②﹣①得,y2﹣y1=x2﹣x1,
∵|x1﹣x2|•|y1﹣y2|=5,
∴|x1﹣x2|=|y1﹣y2|=,
由得x2+bx﹣1=0,
解得,x1=,x2=,
∴|x1﹣x2|=|﹣|=||=,
解得b=±1.
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