解题方法
1 . 如图,已知椭圆
的焦点和上顶点分别为
,我们称
为椭圆
的“特征三角形”.如果两个椭圆的特征三角形是相似的,则称这两个椭圆是“相似椭圆”,且三角形的相似比即为椭圆的相似比. 若椭圆
,直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842e2444f4e0136a82f0a1988d94f273.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/23dbfbdb-7e44-47b9-af17-deba0cd63407.png?resizew=172)
已知椭圆
与椭圆
是相似椭圆,求
的值及椭圆
与椭圆
相似比;
求点
到椭圆
上点的最大距离;
如图,设直线
与椭圆
相交于
两点,与椭圆
交于
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa09740f184022743f260e70d93f45c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3824d9d42a2bd926fbd8f99a2c37eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842e2444f4e0136a82f0a1988d94f273.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/23dbfbdb-7e44-47b9-af17-deba0cd63407.png?resizew=172)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7537bc8d93246e82b027d8b15fb3c434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea024c8f22a8c7c1f5d2e41fe027c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c29a7e8eea08197bf53164a560bee58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1af14f9a53cb0f07d5d28dceba30aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/4a414983-1fb5-4ed5-895a-8551cb1c12e6.png?resizew=171)
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2 . 已知椭圆的焦点分别为
,长轴长为
,设直线
交椭圆于
两点.
求椭圆的方程;
求线段
的中点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020ea7103885c926bad7947a256705e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
3 . 以椭圆
:
的中心
为圆心,
为半径的圆称为该椭圆的“准圆”.设椭圆
的左顶点为
,左焦点为
,上顶点为
,且满足
,
.
(1)求椭圆
及其“准圆”的方程;
(2)若椭圆
的“准圆”的一条弦
与椭圆
交于
、
两点,试证明:当
时,弦
的长为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a363a3f490e78aab74dee5e8cc63fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.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/e0912d895d9df110002bfa347adfd1b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d6f2a41d79a6c6f261d98d32b696e9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8874b310ca7ce7d9909a8bfb6c5a87c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
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4 . 设
,椭圆
:
与双曲线
:
的焦点相同.
(1)求椭圆
与双曲线
的方程;
(2)过双曲线
的右顶点作两条斜率分别为
,
的直线
,
,分别交双曲线
于点
,
(
,
不同于右顶点),若
,求证:直线
的倾斜角为定值,并求出此定值;
(3)设点
,若对于直线
,椭圆
上总存在不同的两点
与
关于直线
对称,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91bf40fb28a0da2d88d570def9ba4780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfbf457f97c06c9c062e809ffdf5b00.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257beb71337358f5ccc57219d9153666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50d653feccc42aba161d0b145510689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5568579340b4a3daf3f01b6dbc4048a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eccd0bda6bfa60e54eb708fcdc6def2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2019-01-16更新
|
493次组卷
|
4卷引用:上海市市北中学2022届高三下学期期中数学试题
上海市市北中学2022届高三下学期期中数学试题上海市实验学校2022-2023学年高二下学期期中数学试题上海市静安区2019届高三上学期期末质量检测数学试题(已下线)重难点06 解析几何-2021年高考数学【热点·重点·难点】专练(上海专用)
名校
5 . 已知
,
,
是椭圆
:
上的三点,其中
的坐标为
,
过椭圆
的中心,且椭圆长轴的一个端点与短轴的两个端点构成正三角形.
![](https://img.xkw.com/dksih/QBM/2020/2/3/2391284884209664/2392028665520128/STEM/029611864bac4519935a58fc5db96ecc.png?resizew=192)
(1)求椭圆
的方程;
(2)当直线
的斜率为1时,求
面积;
(3)设直线
:
与椭圆
交于两点
,
,且线段
的中垂线过椭圆
与
轴负半轴的交点
,求实数
的值.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f809aef106f5da271c4800b261a628f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2020/2/3/2391284884209664/2392028665520128/STEM/029611864bac4519935a58fc5db96ecc.png?resizew=192)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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6 . 如图,在平面直角坐标系
中,已知椭圆
:
,设
是椭圆
上任一点,从原点
向圆
:
作两条切线,分别交椭圆于点
,
.
![](https://img.xkw.com/dksih/QBM/2020/1/31/2389062106529792/2389183410364416/STEM/20bf922ae8404065b2356cca078b20be.png?resizew=259)
(1)若直线
,
互相垂直,且圆心落在第一象限,求圆
的圆心坐标;
(2)若直线
,
的斜率都存在,并记为
,
.
①求证:
;
②试问
是否为定值?若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c03c6b8d7418edf20f474389971352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba593a780698fe887e5f9860401f4e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5fe8def423a0915bba6b4b72add37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/2020/1/31/2389062106529792/2389183410364416/STEM/20bf922ae8404065b2356cca078b20be.png?resizew=259)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1511fecc764a34504b104a69562aa51.png)
②试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c2475f29f388642ac001ef7e854e0ac.png)
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名校
7 . 已知椭圆
的右焦点为
,且过点
. 过焦点
且与
轴不重合的直线与椭圆
交于
、
两点(点
在
轴上方),点
关于坐标原点的对称点为
,直线
、
分别交直线
于
、
两点.
(1) 求椭圆
的方程;
(2) 当直线
的斜率为
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bfa5840675e634a9f5e1f602775e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de261e9b4defbc0be6440397031a87b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2018/9/5/2025938133565440/2042012046696448/STEM/ac6a5f029ff947a7bc855717e8282fae.png?resizew=187)
(1) 求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2) 当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdffaca7c78d569cfeebb80bfc26329.png)
您最近一年使用:0次
名校
8 . 如图,
是椭圆
长轴的两个端点,
是椭圆上与
均不重合的相异两点,设直线
的斜率分别是
.
(1)求
的值;
(2)若直线
过点
,求证:
;
(3)设直线
与
轴的交点为
(
为常数且
),试探究直线
与直线
的交点
是否落在某条定直线上?若是,请求出该定直线的方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3b51b2e06528f326a689b6c69f115b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279921f968ec1782d04dda1a1facbc50.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62ec9eb13c5cfca501ff84357595755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc865417ca32c364908d5068851afae.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9471be1cc5f1e85cc30a78d89e1ca5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/e647a32b-6223-4a19-b66d-ded5e6774faf.png?resizew=232)
您最近一年使用:0次
2018-04-15更新
|
1679次组卷
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7卷引用:上海市育才中学2023届高三上学期期中数学试题
上海市育才中学2023届高三上学期期中数学试题(已下线)高二下期中真题精选(常考60题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)【区级联考】上海市徐汇区2018届高三下学期学习能力诊断(二模)数学试题上海市建平中学2020-2021学年高二下学期3月月考数学试题上海市五校2022-2023学年高二下学期3月联考数学试题(已下线)第2章 圆锥曲线(基础、常考、易错、压轴)分类专项训练(2)(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点2 圆锥曲线中的探索性问题
11-12高二上·山东济宁·阶段练习
名校
9 . 在平面直角坐标系
中,点
到两点
的距离之和等于4,设点
的轨迹为曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
的方程;
(2)设直线
与
交于
两点,
为何值时
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76c5a0c8dff254d560ab24e51e0b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb74745f1d6a291a7422feb93c27dbc.png)
您最近一年使用:0次
2019-12-07更新
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1194次组卷
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14卷引用:上海市杨浦区2016-2017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上海市华东师范大学第三附属中学2015-2016学年高二下学期期中(理)数学试题(已下线)2011-2012学年湖北武汉部分重点中学(五校)高二下期中文科数学卷上海市宝山区扬波中学2017-2018学年高二上学期期末数学试题河北省张家口市第一中学2021届高三(衔接班)上学期期中数学试题(已下线)2011-2012学年山东省邹城二中高二上学期期中文科数学试卷(已下线)2013-2014学年河南省濮阳市高二下学期升级考试理科试卷(A卷)(已下线)2013-2014学年河南省濮阳市高二下学期升级考试理科数学试卷(A)2015-2016学年山东寿光现代中学高二12月月考理数学卷2015-2016学年山东寿光现代中学高二12月月考文数学卷智能测评与辅导[文]-圆锥曲线的综合应用四川省阆中中学2019-2020学年高二4月月考数学(文)试题云南省保山市第九中学2020-2021学年高二9月质量检测数学(文)试题内蒙古呼和浩特市2021-2022学年高二上学期期末考试数学(理)试题
11-12高三上·全国·单元测试
名校
10 . 已知
,
分别是椭圆
长轴的左,右顶点,点
是椭圆的右焦点,点
在椭圆上,且位于
轴的上方,满足
.
(1)求点
的坐标;
(2)若线段
上的一点
到直线
的距离等于
,求椭圆上的点到点
的距离
的最小值.
![](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/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baca70b7370f0695f2a8d43309e572a.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0ffe082c84721fdf556b91040e170d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
您最近一年使用:0次
2020-03-27更新
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308次组卷
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17卷引用:上海市位育中学2020-2021学年高二下学期期中数学试题
上海市位育中学2020-2021学年高二下学期期中数学试题安徽省蚌埠市第一中学2019届高三上学期期中考试数学(文)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 本章复习题广西贵港高中2020-2021学年高二上学期理科期中教学质量监测试题(已下线)2012届大纲版高三上学期单元测试(8)数学试卷(已下线)2011-2012学年贵州省六盘水市第二中学高三11月月考数学理科试卷江苏省盐城市阜宁中学2017-2018学年高二上学期第一次学情调研数学(文)试题甘肃省天水市甘谷县第一中学2017-2018学年高二下学期第一次月考数学(理)试题四川省南充市2019届高三联合诊断数学(文)试题吉林省白城市第四中学2019-2020下学期高二网上阶段检测试卷文科数学试题广东省佛山市2019-2020学年高二上学期统考模拟数学试题江苏省无锡市锡山高级中学2020-2021学年高二上学期10月阶段性考试数学试题甘肃省庆阳市宁县2020-2021学年高二上学期期末数学(理)试题黑龙江省哈尔滨市哈尔滨师范大学附属中学2020-2021学年高二上学期期末考试 数学(理) 试题(已下线)专题11 圆锥曲线的方程综合练习-(新教材)2020-2021学年高二数学单元复习(人教A版选择性必修第一册)内蒙古自治区赤峰市赤峰二中2021-2022学年高二上学期期末数学理科试题沪教版(2020) 选修第一册 领航者 第2章 2.2椭圆 第2课时 椭圆的性质(1)