解题方法
1 . 已知抛物线
,
(1)若该抛物线的焦点
到准线的距离为1,求抛物线的标准方程;
(2)若
,O为坐标原点,斜率为2且过焦点
的直线
交此抛物线于A、B两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
(1)若该抛物线的焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.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/866b81a8384cce4f24867baca2e6820c.png)
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2卷引用:上海市莘庄中学2023-2024学年高二上学期期末数学试题
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解题方法
2 . 椭圆
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
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3 . 已知双曲线
的焦点到渐近线的距离为
,且直线
与双曲线没有公共点,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a9b769d70cb6f29e965c800921c8ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知
为非零实数,则“
”是“
”成立的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb54b1b3617ebc502cb44194cbcd1dc.png)
A.充分非必要条件 | B.必要非充分条件 |
C.充分必要条件 | D.既非充分又非必要条件 |
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2024-01-19更新
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2卷引用:上海市大同中学2023-2024学年高一上学期期末考试试题
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5 . 类似平面解析几何中的曲线与方程,在空间直角坐标系中,可以定义曲面(含平面)
的方程,若曲面
和三元方程
之间满足:①曲面
上任意一点的坐标均为三元方程
的解;②以三元方程
的任意解
为坐标的点均在曲面
上,则称曲面
的方程为
,方程
的曲面为
.已知曲面
的方程为
.
的方程(无需说明理由),指出
平面截曲面
所得交线是什么曲线,说明理由;
(2)已知直线
过曲面
上一点
,以
为方向量,求证:直线
在曲面
上(即
上任意一点均在曲面
上);
(3)已知曲面
可视为平面
中某双曲线的一支绕
轴旋转一周所得的旋转面;同时,过曲面
上任意一点,有且仅有两条直线,使得它们均在曲面
上.设直线
在曲面
上,且过点
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9f353152c7f589c0caf5f964f803ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedd047376c4cf1b9992cd8e4fe20df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](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/f6d287ea4a056d41ba4a1962edd7ad0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9adca4ab5571ac6d246ec24732377ee6.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)已知曲面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7232cb20066a3f4b1ebbf3c44e3a51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
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6 . 斜率为1的直线
被椭圆
截得的弦长为
,则直线
的方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee7999b079f73b469a90326b151a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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7 . 若双曲线C:的焦距长为8,则该双曲线的渐近线方程为
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4卷引用:上海市七宝中学2023-2024学年高二上学期期末考试数学试题
上海市七宝中学2023-2024学年高二上学期期末考试数学试题(已下线)第2章 圆锥曲线(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)陕西省渭南市蒲城县2024届高三第二次对抗赛数学(理科)试题上海市奉贤区2024届高三一模数学试题变式题1-5
8 . 已知椭圆C:
的离心率为
,左、右顶点分别为A、B,过点
的直线与椭圆相交于不同的两点P、Q(异于A、B),且
.
(1)求椭圆C的方程;
(2)若直线AP、QB的斜率分别为
、
,且
,求
的值;
(3)设
和
的面积分别为
、
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d195911a91d12edd5685f6cd963fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dddd06a88839dc33edcea74128743ae.png)
(1)求椭圆C的方程;
(2)若直线AP、QB的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc0ee0a95fab04edf648026f14b9ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a551505ae42b49904bab59b17012d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9c5ae63072e1684cf1c242c8133d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59c4295f918205f5598ecc9a96d8867.png)
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4卷引用:上海市七宝中学2023-2024学年高二上学期期末考试数学试题
解题方法
9 . 双曲线
的渐近线方程为
,则实数
的值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2597e03b5289a0d6fb3b9074623c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3051f43ac48c0a730a791b8a93ad37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 已知空间向量
.若
四点共面,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ebccc9df7e0c15625479a7732cce4d.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e5f33dcca7ec967c49cbd9491afe0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a0889f0f80987c260cce05be4c84b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ebccc9df7e0c15625479a7732cce4d.png)
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