解题方法
1 . 已知集合
,
.
(1)若
,求
;
(2)设
,
,若
是
的必要不充分条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22ed8e979c0c897db6a91442732843c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4453c51bdfba6f899eccfaf34f952db.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc11e9183ffccd297df4a1c18618bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218c5309e534904dc6bf768074965239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
2 . 如图,已知
分别为双曲线
的左、右焦点,P为第一象限内一点,且满足
,线段
与双曲线C交于点Q,若
,则双曲线 C的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e56c9c9a-c4e3-4fe8-90a3-d0f3ef16f13a.png?resizew=183)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a63a221e7ed2b5eb5b03241860e26f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f661844844bceeccf7770876b9930edd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e56c9c9a-c4e3-4fe8-90a3-d0f3ef16f13a.png?resizew=183)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
3 . 如图,在几何体
中,四边形
为等腰梯形,且
,
,四边形
为矩形,且
,M,N分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2021/3/14/2677644320817152/2683136306356224/STEM/1b1487a7-7961-4c96-9331-ba013e4aaa5b.png)
(1)求证:
平面
;
(2)若直线
与平面
所成的角为60°,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6045266f6db39e41b7abde762d9e9a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4e574c9d139615d991a168cfbf63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6fea7f65f39b3e22aa5ad6cd1af5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2021/3/14/2677644320817152/2683136306356224/STEM/1b1487a7-7961-4c96-9331-ba013e4aaa5b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1674add0f4a1a24f5ed893b1c5d0.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1674add0f4a1a24f5ed893b1c5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
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解题方法
4 . 已知A,B分别为椭圆
的左右顶点,E为椭圆C的上顶点,F为椭圆C的右焦点,E与F关于直线
对称,
的面积为
,过
的直线交椭圆C于两点M,N(异于A,B两点).
(1)求椭圆C的方程;
(2)证明:直线
与
的交点P在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5829fe58856c0290757a40e26cda072.png)
(1)求椭圆C的方程;
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
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5 . 已知A,B是椭圆
的左、右顶点,C为E的上顶点,
.
(1)求椭圆的方程;
(2)若M,N,P是椭圆E上不同的三点,且坐标原点O为
的重心,试探究
的面积是否为定值?若是,求出这个定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60906fb8f76022953cdae6ac61104737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fb76b11ff141ccd75a163f7def5357.png)
(1)求椭圆的方程;
(2)若M,N,P是椭圆E上不同的三点,且坐标原点O为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23b488f961d9fde37feb7f5c497c0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23b488f961d9fde37feb7f5c497c0d9.png)
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解题方法
6 . 已知双曲线
的左、右焦点分别为
、
,以
为直径的圆与双曲线的一条渐近线交于点
,若线段
交双曲线于点
,且
,则双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.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/1f95a62596525307343da7ff4b86cde8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956c0b3335922c0586a101dfdb8fdea0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知抛物线
的焦点为F,P是抛物线上一点,若
,则P点的横坐标为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360d86f0ec1c4d9d0dfc06a9064db0b1.png)
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8 . 设命题
:实数
满足
;命题
:曲线
表示双曲线.若p为假命题,
为真命题,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143e9daff5e4f18d8791a7d508d60642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357dcfc6aadbb79cb58ab672c2a30b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f675824e539f50cec53120959d32e554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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9 . 已知直线
经过抛物线
的焦点,与抛物线交于
,且
,点
是弧
(
为原点)上一动点,以
为圆心的圆与直线
相切,当圆
的面积最大时,圆
的标准方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd5f2221306f105938869e6eea62acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad1e1c3ba382a47a92b24c5f15c1eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c6b8d95b188074ae972314973d6b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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10 . 命题“
,
”的否定是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02491f9709f00a1bc169278fbe01f576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014ad67738b68ab6fb14b933cd1199eb.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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