名校
1 . 如果直线
经过双曲线
的中心,且与该双曲线不相交,则
的斜率的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c0bda0f3eb049672095223913a53be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
2 . 双曲线的方程是.求过点
作直线
,使其被双曲线截得的弦恰被
点平分,求直线
的方程.
您最近一年使用:0次
名校
3 . 已知椭圆
的左,右焦点分别为
,
,上顶点为
,且
.
(1)求
的离心率;
(2)射线
与
交于点
,且
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be0160e528ddd1d2a7f20ad378879c6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082ed765c7e1162e6fb1d6bdf547afe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
您最近一年使用:0次
2024-03-14更新
|
1464次组卷
|
2卷引用:福建省福州外国语学校2023-2024学年高二下学期4月期中考试数学试题
解题方法
4 . 已知双曲线方程为
(
),若直线
与双曲线左右两支各交一点,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423db9ff20877e08b9ea37df4bd09b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c6d3c99b7004603ba9ea9c341b8b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 已知抛物线
:
的焦点为
,直线
与
交于
,
两点.
(1)求
的值;
(2)若
上存在点
,使
的重心恰为
,求
的值及点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1794105046d96bbc3a84f868fc197e4.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)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85af6eaff9a4e3e9af4e9c1f4f7b996.png)
(2)若
![](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/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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名校
解题方法
6 . 已知椭圆
的右焦点
与抛物线
的焦点重合,且椭圆的离心率为
.
(1)求椭圆
的方程;
(2)过抛物线焦点的直线和抛物线相交于M,N两点,
,求直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过抛物线焦点的直线和抛物线相交于M,N两点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9602114f45bdcb304e02710ae7bc0e08.png)
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解题方法
7 . 已知双曲线
,则双曲线
的离心率为______ ;直线
与双曲线相交于
两点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411c29f9baf01259a1093fe46774f11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
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解题方法
8 . 已知点
在抛物线
上,则点
到直线
的距离和到直线
的距离之和的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4e70ad712d8d6e2066e38093ad732e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41ccf22ae1da0f62c6e36e724cb4382.png)
您最近一年使用:0次
2024高二·全国·专题练习
解题方法
9 . 已知双曲线
,直线
,试确定实数k的取值范围,使:
(1)直线l与双曲线有两个公共点;
(2)直线l与双曲线有且只有一个公共点;
(3)直线l与双曲线没有公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4334e343daae170f14d086661bc5792a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72eeed455051e355653892f1f8bbfba5.png)
(1)直线l与双曲线有两个公共点;
(2)直线l与双曲线有且只有一个公共点;
(3)直线l与双曲线没有公共点.
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10 . 已知点
为抛物线
:
的焦点,点
在抛物线
上,且
.
(1)求抛物线
的方程;
(2)已知点
,过点
的直线交抛物线于
、
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921502954d8f4c6e58a95487018a8a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7bf417767442935d2b9e49d18fbea79.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad434a7febc9d1491e73f51b86cd588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/28f6fe7f033e623471c1217652acd042.png)
您最近一年使用:0次
2024-03-01更新
|
783次组卷
|
2卷引用:山西省太原市2023-2024学年高二上学期期末数学试题