1 . 过点
作圆O:
的两条切线,则两条切线夹角的正弦值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
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2 . 设椭圆C:
(
)的两个焦点是
和
(
),且椭圆C与圆
有公共点.
(1)求实数a的取值范围;
(2)若椭圆C上的点到焦点的最长距离为
,求椭圆C的方程;
(3)对(2)中的椭圆C,直线:
(
)与C交于不同的两点M,N,若线段
的垂直平分线恒过点
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dae6629e0dbf18af625cb804874afb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26edd7d076460e7aa7e8f319cb2be370.png)
(1)求实数a的取值范围;
(2)若椭圆C上的点到焦点的最长距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
(3)对(2)中的椭圆C,直线:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71885f023172807ad43f2c9a670aa960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3 . 已知点M为双曲线C:
上任意一点,过点M分别作C的两条渐近线的垂线,垂足分别为A,B,则四边形
(O为原点)的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4334e343daae170f14d086661bc5792a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6c989fd224866658230526892e2bcb.png)
A.4 | B.2 | C.1 | D.![]() |
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4 . 已知圆
:
与圆
:
相交于A,B两点,则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376bc360486059a9674a964d031e9ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28da6766230aeb546a2588daf93958ff.png)
A.两圆的相交弦所在直线方程为![]() |
B.两圆的公共弦长为![]() |
C.经过A,B两点,且过原点的圆的方程为![]() |
D.P为![]() ![]() ![]() |
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解题方法
5 . 已知双曲线
(
,
)的右焦点与抛物线
(
)的焦点重合,抛物线的准线交双曲线于M,N两点,交双曲线的渐近线于P,Q两点.若
,则双曲线的离心率为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.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/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04461d48543cbd979918777065802b68.png)
您最近一年使用:0次
2024-02-06更新
|
257次组卷
|
3卷引用:内蒙古自治区锡林郭勒盟2023-2024学年高二上学期期末教学质量检测数学试卷
内蒙古自治区锡林郭勒盟2023-2024学年高二上学期期末教学质量检测数学试卷江西省上饶市沙溪中学2023-2024学年高二上学期期末数学试题(已下线)3.3.1 抛物线及其标准方程【第三练】“上好三节课,做好三套题“高中数学素养晋级之路
解题方法
6 . 已知圆C经过点
和点
,且圆心在y轴上,则圆C的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1282cc43ebf4b459832fec04d805989.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 直线
过抛物线C:
(
)的焦点F,且与C交于A,B两点,
为C的准线,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92020e8ae02f1b51d5c8d84e12bffa49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.准线![]() ![]() |
您最近一年使用:0次
2024-01-26更新
|
223次组卷
|
2卷引用:内蒙古自治区锡林郭勒盟2023-2024学年高二上学期期末教学质量检测数学试卷
解题方法
8 . 已知等比数列
的各项均为正数,
,
.
(1)求数列
的通项公式.
(2)若
,求数列
的前n项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e336e14821c5d679b1532b0625797a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72319947da079ad3fd908ee39459fe1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee90c6611c96d493ce52637a4ed4ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
您最近一年使用:0次
解题方法
9 . 已知线段AB的端点
,端点A在圆
上运动,线段AB的中点为M.
(1)求动点M的轨迹方程;
(2)设动点M轨迹的中心为C,过点
的直线l与M的轨迹交于P,Q两点,当
时,求l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266c42a10c13c00114ae371b2d9f728d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7a66df197e63b3120bf3aa3a367b0f.png)
(1)求动点M的轨迹方程;
(2)设动点M轨迹的中心为C,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f30b2646041302c125188f26c102be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052432439e3482ebbbf8cf9604c8d537.png)
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10 . 过抛物线C:
(
)的焦点F且垂直于y轴的直线与C交于A,B两点,若
.
(1)求抛物线的方程;
(2)设直线
与抛物线C交于P,Q两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
(1)求抛物线的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
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