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1 . 圆O:x2+y2=9上的动点P在x轴、y轴上的射影分别是P1,P2,点M满足
.
(1)求点M的轨迹C的方程;
(2)点A(0,1),B(0,﹣3),过点B的直线与轨迹C交于点S,N,且直线AS、AN的斜率kAS,kAN存在,求证:kAS•kAN为常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d00285706446f20e0955adb5f0de582.png)
(1)求点M的轨迹C的方程;
(2)点A(0,1),B(0,﹣3),过点B的直线与轨迹C交于点S,N,且直线AS、AN的斜率kAS,kAN存在,求证:kAS•kAN为常数.
您最近一年使用:0次
2019-05-30更新
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1657次组卷
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5卷引用:广东省深圳市宝安中学2019-2020学年高二上学期期中数学试题
广东省深圳市宝安中学2019-2020学年高二上学期期中数学试题【市级联考】湖南省益阳市2019届高三上学期期末考试数学(理)试题【市级联考】山东省泰安市教科研中心2019届高三考前密卷数学(理)试题(已下线)专题06 解析几何中的定点、定值问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖山东省烟台市莱州市第一中学2020-2021学年高二上学期12月月考数学试题
2 . 已知点
是圆
上一动点,作
轴,垂足为
,且
.
(1)求动点
的轨迹
的方程;
(2)过点
斜率为
的直线
交曲线
于
,
两点,直线
,
的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f00d0ff8dd38da17167cf9b789eec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064c89ea15fbb4f45bed31f77c2730a3.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfec83404d339e89ccbe357b0a111fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d91b6a7f165b0e2929a735b79be8a3.png)
您最近一年使用:0次
2018-06-06更新
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818次组卷
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2卷引用:【全国市级联考】广东省汕头市2016-2017学年高二下学期期末教学质量监测文科数学
3 . 如图,在平面直角坐标系
中,直线
与直线
之间的阴影部分记为
,区域
中动点
到
的距离之积为1.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/efc1137f-06a5-4dcf-b3a9-42639ce163ea.png?resizew=174)
(1)求点
的轨迹
的方程;
(2)动直线
穿过区域
,分别交直线
于
两点,若直线
与轨迹
有且只有一个公共点,求证:
的面积恒为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bce9bdeb6b4e2401d9907f4e3f0c540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc20ecfb48de46ccba10337431d7fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/efc1137f-06a5-4dcf-b3a9-42639ce163ea.png?resizew=174)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8189f7b0ffe4d20bf0fad43b4ed589.png)
您最近一年使用:0次
2018-01-20更新
|
824次组卷
|
8卷引用:【全国百强校】广东仲元中学2017-2018学年高二下学期期中考试数学(理)试题
【全国百强校】广东仲元中学2017-2018学年高二下学期期中考试数学(理)试题河南省安阳市2018届高三第一次模拟考试数学(理)试题河南省安阳市2018届高三第一次模拟考试数学(文)试题(已下线)2018年高考数学备考中等生百日捷进提升系列(综合提升篇) 专题05 解析几何解答题人教B版(2019) 选择性必修第一册 过关斩将 全书综合测评(已下线)3.2.1 双曲线及其标准方程-2020-2021学年高二数学课时同步练(人教A版选择性必修第一册)(已下线)3.2.1 双曲线的标准方程(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)3.2.1 (分层练)双曲线及其标准方程-2021-2022学年高二数学考点同步解读与训练(人教A版2019选择性必修第一册)
解题方法
4 . 如图,已知圆
,设A为圆C与x轴负半轴的交点,过点A作圆C的弦AM,并使弦AM的中点恰好落在y轴上.
![](https://img.xkw.com/dksih/QBM/2016/2/26/1572500601774080/1572500607655936/STEM/227f82d3d93f48e39efa898d94a75d5d.png?resizew=158)
(1)当r在
内变化时,求点M的轨迹E的方程;
(2)已知定点
和
,设直线PM、QM与轨迹E的另一个交点分别是
.求证:当M点在轨迹E上变动时,只要
都存在且
,则直线
恒过一个定点,并求出这个定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e28d333929a88ed1135f8785d017b8.png)
![](https://img.xkw.com/dksih/QBM/2016/2/26/1572500601774080/1572500607655936/STEM/227f82d3d93f48e39efa898d94a75d5d.png?resizew=158)
(1)当r在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
(2)已知定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada785fae54b7aa18e8f60cad8d887be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1777a71d3ba5d11534de2e2319c14d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c07fb3f5689102322a77f848370445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c07fb3f5689102322a77f848370445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d13c7dfe85ea3ef8c7cd06224651a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dedd84baa5219a2af415be51947c301.png)
您最近一年使用:0次
5 . 如图,设点A,B的坐标分别为(-
,0),(
),直线AP,BP相交于点P,且它们的斜率之积为-
.
(1)求P的轨迹方程;
(2)设点P的轨迹为C,点M、N是轨迹为C上不同于A,B的两点,且满足AP∥OM,BP∥ON,求证:△MON的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f8c3ba00c59e0634ed10fa85289de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e863e5d130d544b8ba49e75d14371e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0e7bfbd56fe73dfe04c04da749d942.png)
(1)求P的轨迹方程;
(2)设点P的轨迹为C,点M、N是轨迹为C上不同于A,B的两点,且满足AP∥OM,BP∥ON,求证:△MON的面积为定值.
![](https://img.xkw.com/dksih/QBM/2019/3/26/2168943123709952/2170165277933568/STEM/388cb288d813421bb90c1714f657518d.png?resizew=239)
您最近一年使用:0次
2017-02-08更新
|
1314次组卷
|
3卷引用:【校级联考】广东省六校2019届高三第三次联考理科数学试题