名校
1 . 设点
是曲线
上一点,则点
到直线
最小的距离为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec087e5a282a4bfa9fba07e456695c9.png)
您最近一年使用:0次
2024-05-08更新
|
235次组卷
|
3卷引用:广东省广州市执信中学2023-2024学年高二下学期5月月考数学试卷
名校
解题方法
2 . 已知双曲线
(
,
)的焦距为
,且
经过抛物线
的焦点.记
为坐标原点,过点
的直线
与
相交于不同的两点
,
.
(1)求
的方程;
(2)证明:“
的面积为
”是“
轴”的必要不充分条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c9c1fc1ba184e358a80bdd7538d92a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.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)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de68db2706156f1ee17e24f843b40cd.png)
您最近一年使用:0次
2024-05-08更新
|
203次组卷
|
2卷引用:广东省梅州市部分学校2023-2024学年高二下学期4月期中联考数学试题
2024·北京·模拟预测
名校
解题方法
3 . 已知椭圆
的左顶点为
,两个焦点与短轴一个顶点构成等边三角形,过点
且与
轴不重合的直线
与椭圆交于
两点.
(1)求椭圆
的方程;
(2)若过点
且平行于
的直线交直线
于点
,求证:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2375a27ead9549550676d4e6a2b47243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f33f27e2c96f019bc9be1ac55e52f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a61d77911527508524874b212a0937d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
您最近一年使用:0次
名校
解题方法
4 . 已知动圆
(
为圆心)过定点
,且与定直线
相切.
(1)求动圆圆心
的轨迹方程;
(2)设过点
且斜率为
的直线与(1)中的曲线交于
、
两点,求
;
(3)设点
是
轴上一定点,求
、
两点间距离的最小值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47153fdd73c0661fa460130082e30929.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/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6214b125be1a9950a6c3d5999829d7.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7041b9af5b111b67a0eb98430ceaa17.png)
您最近一年使用:0次
2024-04-24更新
|
218次组卷
|
2卷引用:广东省广州市育才中学2023-2024学年高二下学期期中数学试题
名校
解题方法
5 . 已知
为坐标原点,抛物线
的焦点为
,过
的直线
与
交
,
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](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/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
A.![]() | B.若![]() ![]() ![]() |
C.若直线![]() ![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 对称轴都在坐标轴上的双曲线过点
,
,斜率为
的直线
过点
.
(1)求双曲线的标准方程;
(2)若直线
与双曲线有两个交点,求斜率
的取值范围;
(3)是否存在实数
使得直线
与双曲线交于A,B两点,且点P恰好为AB中点?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3f986a4f053c576c8a58c7debc8829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b55968d5f6b29626b1303e3cfe3132f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd064fc631163ed5e461887aa53cf197.png)
(1)求双曲线的标准方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
7 . 已知双曲线
的左焦点为
,方向向量为
的直线l过
与双曲线左,右两支分别交于
,
两点且
,则双曲线离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fe34d47ef23e8884a5c0404e54ef54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/5c2e97d6fb41ec5eccfd1fe8f72a92a6.png)
您最近一年使用:0次
名校
解题方法
8 . 已知点F是抛物线C:
的焦点,过点F的直线l交抛物线C于P,Q两点,过点P作C的准线的垂线,垂足为M,O为坐标原点.
(1)证明:Q,O,M三点共线;
(2)若
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
(1)证明:Q,O,M三点共线;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80a362c99c725a66f7565f43c4dc16a.png)
您最近一年使用:0次
2024-04-16更新
|
152次组卷
|
2卷引用:广东省茂名市高州中学2023-2024学年高二下学期5月第一次模拟数学试卷
名校
解题方法
9 . (多选)已知
,
分别为椭圆C:
的左、右焦点,P为椭圆上任意一点(不在x轴上),
的内切圆与
切于点M,过点
的直线l与C交于A,B两点,则( )
![](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/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355dffb42861f3e297694f4be77c694c.png)
A.![]() |
B.![]() |
C.![]() |
D.若Q为![]() ![]() |
您最近一年使用:0次
2024-04-16更新
|
348次组卷
|
2卷引用:广东省茂名市高州中学2023-2024学年高二下学期5月第一次模拟数学试卷
解题方法
10 . 已知双曲线
的一条渐近线方程为
,焦点到渐近线的距离为1.
(1)求双曲线
的标准方程与离心率;
(2)已知斜率为
的直线
与双曲线
交于
轴上方的
两点,
为坐标原点,直线
的斜率之积为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0ad4902b595ea0e21641145f4e41c9.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e165ecb6f59aff040ac62edd49cc5551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次