名校
解题方法
1 . 已知点
为双曲线
上的动点.
(1)判断直线
与双曲线的公共点个数,并说明理由;
(2)(i)如果把(1)的结论推广到一般双曲线,你能得到什么相应的结论?请写出你的结论,不必证明;
(ii)将双曲线
的两条渐近线称为“退化的双曲线”,其方程为
,请利用该方程证明如下命题:若
为双曲线
上一点,直线
:
与
的两条渐近线分别交于点
,则
为线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea74737939c0f94c91229a7098f36ec.png)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e314fafd906934931d5cdfb4ecad2fca.png)
(2)(i)如果把(1)的结论推广到一般双曲线,你能得到什么相应的结论?请写出你的结论,不必证明;
(ii)将双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e56464f202655f76b90e0f89e91be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cad114964b344e7c9b3903a21354e4.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/006d86d8f686ca9afaa3ef23a519728a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2024-03-04更新
|
1265次组卷
|
5卷引用:广东省汕头市2024届高三第一次模拟考试数学试题
广东省汕头市2024届高三第一次模拟考试数学试题(已下线)第26题 圆锥曲线压轴大题(1)(高三二轮每日一题)(已下线)大招4 圆锥曲线创新问题的速破策略江苏省盐城市五校联考2023-2024学年高二下学期第一次学情调研检测(3月)数学试题山东省烟台市牟平第一中学2023-2024学年高二下学期3月限时练(月考)数学试题
解题方法
2 . 已知
为双曲线
上一点,
分别为双曲线
的左、右顶点,且直线
与
的斜率之和为
.
(1)求双曲线
的方程;
(2)不过点
的直线
与双曲线
交于
两点,若直线
的倾斜角分别为
和
,且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00d5d8cc31aaca7fc2eafb99eac7629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)不过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c287201dc8f4b7e1a8dd41920654656.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/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c46c36d132399a9504054a743016ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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3 . 已知直线
,动点
分别在直线
上,
,
是线段
的中点,记点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)已知点
,过点
作直线
与曲线
交于不同的两点
,线段
上一点
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37659c39c4f4d6933e4b49df20af7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699fc9b7e879af4866aaa07848dfb423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/b94469fd19f40116e2dec334919d6586.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f40d5459e1385ab7d829ea96ca0b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c708a642769de87e08886d98f14f13c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a84af713ec9898211637cfa1b0ef3b2.png)
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名校
解题方法
4 . 双曲线具有如下性质:双曲线在任意一点处的切线平分该点与两焦点连线的夹角.设
为坐标原点,双曲线
的左右焦点分别为
,右顶点
到一条渐近线的距离为2,右支上一动点
处的切线记为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9514e33f57fcd4dc111c83f812d89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.双曲线![]() ![]() |
B.双曲线![]() ![]() |
C.当![]() ![]() |
D.过点![]() ![]() ![]() |
您最近一年使用:0次
2024-03-03更新
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1132次组卷
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3卷引用:广东省广州市天河区2024届高三毕业班综合测试(二)数学试卷
解题方法
5 . 直线
与椭圆
交于A、B两点(点
在第一象限),过点
作
轴的垂线,垂足为E,AE的中点为
,设直线
与椭圆的另一交点为
,若
,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54dda146b8b3e50da6bfbf7124a7f08.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-03-03更新
|
898次组卷
|
3卷引用:广东省2024届高三新改革数学适应性训练六(九省联考题型)
解题方法
6 . 已知椭圆
的左、右顶点分别是
,
,点
在椭圆
上,
是椭圆
上异于点
,
的动点,且直线
,
的斜率之积为
.
(1)求椭圆
的标准方程.
(2)过点
的直线
与椭圆
交于
,
(异于
,
)两点,直线
与
交于点
,试问点
是否恒在一条直线上?若是,求出该直线方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/27208f7c8d1f32587bcb0a52dbc40c56.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/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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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名校
7 . 已知双曲线
的左、右焦点分别为
,过点
的直线与双曲线
的右支交于
两点,若
,且双曲线
的离心率为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df0be6a014b2bd07e265b4cb1ee1b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231f5e366e03c8f8ff6834228ec5ed2f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-29更新
|
4007次组卷
|
5卷引用:广东省深圳市2024届高三第一次调研考试数学试卷
广东省深圳市2024届高三第一次调研考试数学试卷广东省广州市白云中学2023-2024学年高三下学期零模(3月月考)数学试题安徽省江南十校2024届高三联考信息卷数学模拟预测卷(一)(已下线)专题08 圆锥曲线 第一讲 圆锥曲线的方程与性质(解密讲义)湖南省邵阳市邵东市第一中学2023-2024学年高二下学期3月月考数学试题
解题方法
8 . 已知双曲线
的左、右焦点分别为
,
,过点
的直线
与双曲线
的两支分别交于
,
两点.若
,且
,则双曲线
的离心率是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/16e6ca678726753ee6ca48b846c44a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f68412783359c1a90956ae7cb1c8923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2024-02-28更新
|
427次组卷
|
3卷引用:广东省百校联考2023-2024学年高三下学期开学考试数学试题
广东省百校联考2023-2024学年高三下学期开学考试数学试题广东省茂名市华南师范大学附属茂名滨海学校2023-2024学年高二下学期第一次段考(4月)数学试题(已下线)专题7 圆锥曲线与定比分点法【练】(压轴小题大全)
9 . 已知椭圆
的方程为
,右焦点为
,且离心率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
的方程;
(2)过点
的直线
与椭圆
交于
两点,证明:圆
恒与以弦
为直径的圆相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e26f8f60811c0e214939cdffd3206b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-02-28更新
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2卷引用:广东省2024届高三下学期开学考试数学试题
10 . 曲线
上动点
与
构成
,若
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67d93773ed34cfe79fd47025c9dac1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51296b06e4f0ac74bea949ce2d9faa6a.png)
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