名校
解题方法
1 . 在平面直角坐标系
中,对于直线
和点
、
,记
,若
,则称点
、
被直线
分隔,若曲线
与直线
没有公共点,且曲线
上存在点
、
被直线
分隔,则称直线
为曲线
的一条分隔线.
(1)判断点
是否被直线
分隔并证明;
(2)若直线
是曲线
的分隔线,求实数
的取值范围;
(3)动点
到点
的距离与到
轴的距离之积为
,设点
的轨迹为曲线
,求证:通过原点的直线中,有且仅有一条直线是
的分隔线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fa0e0526598c4140789f6328daac9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653fe002a6d9968d6b1d2e7ec36d178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4869bf9983f59598ca7954fd7e89b66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b3d5b330a1e9746267f1a80482e435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a93e8201cd8010f841a105bc9afd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76e726cd6ff947e0ae20c07ebfa8bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348aca26e61218d251581e21c1129a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378e03d75c73c8ca71f991a8c07729a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
解题方法
2 . 已知双曲线
,经过点
的直线
与该双曲线交于
两点.
(1)若
与
轴垂直,且
,求
的值;
(2)若
,且
的横坐标之和为
,证明:
.
(3)设直线
与
轴交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e250158df0fcb0b51013bd626545e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac8fa800c00933279f2b20e5034438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138c0f0b71a955d0a4f249d57b53d5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a563c50a7f6d10fa46339d7107fc85e.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb6ee119dc122c6bda124041812a2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
2020-05-20更新
|
508次组卷
|
5卷引用:2020届上海杨浦区高三二模数学试题
2020届上海杨浦区高三二模数学试题(已下线)热点04 平面向量、复数-2021年高考数学【热点·重点·难点】专练(上海专用)上海市致远高中2020-2021学年高二上学期12月月考数学试题上海市同济大学第二附属中学2024届高三上学期期中数学试题西藏拉萨市部分学校2023-2024学年高二上学期期末模拟数学试题(理科)
名校
3 . 在平面直角坐标系
中,对于直线
和点
、
,记
,若
,则称点
,
被直线l分隔,若曲线C与直线l没有公共点,且曲线C上存在点
,
被直线l分隔,则称直线l为曲线C的一条分隔线.
(1)求证:点
、
被直线
分隔;
(2)若直线
是曲线
的分隔线,求实数
的取值范围;
(3)动点M到点
的距离与到y轴的距离之积为1,设点M的轨迹为E,求E的方程,并证明y轴为曲线E的分隔线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fa0e0526598c4140789f6328daac9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b291c8f35ccdab81c474f286f6dc7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5e2c8b545bc2a67ee4b024ab219b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e30645f36e8628b9e25d53598d5174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348aca26e61218d251581e21c1129a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)动点M到点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378e03d75c73c8ca71f991a8c07729a.png)
您最近一年使用:0次
2019-12-12更新
|
320次组卷
|
6卷引用:上海市新中高级中学2017-2018学年高二下学期期中数学试题
上海市新中高级中学2017-2018学年高二下学期期中数学试题上海市杨浦区2016-2017学年高二下学期期中数学试题沪教版(上海) 高二第二学期 新高考辅导与训练 第12章 圆锥曲线 本章复习题(已下线)重组卷03(已下线)专题24 解析几何解答题(文科)-1(已下线)专题24 解析几何解答题(理科)-3
名校
4 . 如图,已知曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8664e94c5793590f8d478e20908317c6.png)
,曲线
,P是平面上一点,若存在过点P的直线与
都有公共点,则称P为“
型点”.
![](https://img.xkw.com/dksih/QBM/2020/1/9/2373535080144896/2373593427968000/STEM/e4434afaff9a491eb01394e08d051e00.png?resizew=173)
(1)若
,
时,判断
的左焦点
是否为“
型点”,并说明理由;
(2)设直线
与
有公共点,求证
,进而证明原点不是“
型点”;
(3)若圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd432589cb00c29cac1806288e99ed0.png)
内的任意一点都不是“
型点”,试写出a、b满足的关系式,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8664e94c5793590f8d478e20908317c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4b0a3b2e59998deacae94069bcc5ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f844bab7df19b7dc383019f5fb34e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880248fa1259b2600a87f09a61287d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
![](https://img.xkw.com/dksih/QBM/2020/1/9/2373535080144896/2373593427968000/STEM/e4434afaff9a491eb01394e08d051e00.png?resizew=173)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fadd2e6f0aa16c2c466c904474ffc79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553288bc51ba6174dab2e0175d2df90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
(3)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd432589cb00c29cac1806288e99ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9314b34791285525ebef09afa9d2b922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
您最近一年使用:0次
真题
名校
5 . 如图,已知曲线
,曲线
,P是平面上一点,若存在过点P的直线与
都有公共点,则称P为“C1—C2型点”.
(1)在正确证明
的左焦点是“C1—C2型点”时,要使用一条过该焦点的直线,试写出一条这样的直线的方程(不要求验证);
(2)设直线
与
有公共点,求证
,进而证明原点不是“C1—C2型点”;
(3)求证:圆
内的点都不是“C1—C2型点”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f63dee0fb484e63eb3a8baebcdf46f1.png)
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571296931315712/1571296936722432/STEM/3ed6c0368dc94e10afd48a28c75e801f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/30/854d5f50-0404-48a2-ba83-49ad3c2727e1.png?resizew=168)
(1)在正确证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553288bc51ba6174dab2e0175d2df90a.png)
(3)求证:圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28123e129b6426c9a5f31ad8ec2465b.png)
您最近一年使用:0次
2019-01-30更新
|
2081次组卷
|
6卷引用:2013年全国普通高等学校招生统一考试理科数学(上海卷)
真题
6 . 在平面直角坐标系
中,对于直线
:
和点
记
若
<0,则称点
被直线
分隔.若曲线C与直线
没有公共点,且曲线C上存在点
被直线
分隔,则称直线
为曲线C的一条分隔线.
⑴求证:点
被直线
分隔;
⑵若直线
是曲线
的分隔线,求实数
的取值范围;
⑶动点M到点
的距离与到
轴的距离之积为1,设点M的轨迹为E,求
的方程,并证明
轴为曲线
的分割线.
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/146bc338f0cb4b9eac729e20a2d84c9d.png?resizew=28)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/8cc7f97b973d4055babec655488c3dc7.png?resizew=9)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f6e1f67dc15c3cf135a78af95c70fe.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/4798c1132a6e4f51b43cf3f27e5e55d2.png?resizew=132)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d9dbc16d2f63153fdd7b4e612ebfd7.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/799cdc6ca82444bba6e38ded9e4f05a9.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/0ee6677792774e1f92376a3cc9cdcf04.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/8cc7f97b973d4055babec655488c3dc7.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/8cc7f97b973d4055babec655488c3dc7.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/d6ed1f43183149358b54022127d1376c.png?resizew=44)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/8cc7f97b973d4055babec655488c3dc7.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/8cc7f97b973d4055babec655488c3dc7.png?resizew=9)
⑴求证:点
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/4db3073bd68f40a48ff1be5d04e1149e.png?resizew=137)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/fc8a60b8c323475fafee5e37ae437883.png?resizew=80)
⑵若直线
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/28005b52bdec46a5a73f547fec3b5fca.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/c336db074c384094989b4af9e793011f.png?resizew=80)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/1814601f310e4e1d8da6d2739f5a7de5.png?resizew=13)
⑶动点M到点
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/2b948a7ab1d644cdb681998277c3f8b3.png?resizew=56)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/f8696ed58b464e0193e6d72fe9643684.png?resizew=15)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1571792460980224/1571792597475328/STEM/f8696ed58b464e0193e6d72fe9643684.png?resizew=15)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2019-01-30更新
|
2070次组卷
|
2卷引用:2014年全国普通高等学校招生统一考试理科数学(上海卷)
名校
7 . 如图,已知曲线
,曲线
,
是平面上一点,若存在过点
的直线与
都有公共点,则称
为“
型点”.
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237242368/STEM/e2692fbc1f4647a0a8b17efc77414ca8.png?resizew=212)
(1)证明:
的左焦点是“
型点”;
(2)设直线
与
有公共点,求证:
,进而证明原点不是“
型点”;
(3)求证:
内的点都不是“
型点”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f63dee0fb484e63eb3a8baebcdf46f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88956e6ba9a7e1d23fabc6707fc3da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880248fa1259b2600a87f09a61287d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabe1a4f2ae90e0ff2bbfe913404cea4.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237242368/STEM/e2692fbc1f4647a0a8b17efc77414ca8.png?resizew=212)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1f54ccf474ea17a7fe62a1b6f0e87.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db94a845b19c6ee907a2e566cc4da9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1f54ccf474ea17a7fe62a1b6f0e87.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fac7fedc3d5ebe2e396075e7d2caa51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1f54ccf474ea17a7fe62a1b6f0e87.png)
您最近一年使用:0次
8 . 已知双曲线
的实轴长为2,离心率为
,圆
的方程为
,过圆
上任意一点
作圆
的切线
交双曲线于
,
两点.
的方程;
(2)求证:
;
(3)若直线
与双曲线的两条渐近线的交点为
,
,且
,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce5d2e7f7ed678e14e2c1d1297cef34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f788fb0059b7356dc6c7811f46057e66.png)
(3)若直线
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95b304c56842d7c12f56b1b809d7b0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
9 . 已知实数x,y满足方程
.
(1)求
的值;
(2)设
与
是方程组
两组不同的解,其中
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1beb6812158ca2a3082bd13ca07578f0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1afbc87ccffbc98b9ab58df8c69bee.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99307ab4373fbe72422ae5aa980db61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41039d45e37899d233232de3d802b105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccee8eb181dc117834582bc433eca559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab3cf6695638d5bcd26580174d7cbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
您最近一年使用:0次
10 . 已知抛物线
:
与双曲线
:
相交于点
.
(1)若
,求抛物线
的准线方程;
(2)记直线l:
与
、
分别切于点M、N,当p变化时,求证:
的面积为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3a4f9f9ae0a23a09a780f3073d132a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b79ca81f286d8aeed52f91ee13ce0d8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8faa47316e8d6c9631775a9d170bd26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)记直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2ca3d56b93b5f218eaebb87045cd2b.png)
您最近一年使用:0次