解题方法
1 . 已知椭圆
:
的四个顶点
,
,
,
所构成的菱形面积为6,且椭圆的焦点为抛物线
与
轴的交点.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于
,
两点,若
,且
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039366bdd4e28f1fb4fd6c7ba728b6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af25930b4a26ba263ff8bd285ba32c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b671cdde6baf9ab577330696ca8ff121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d303c32af8831735d4e0f86fa45874.png)
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2 . 已知椭圆
:
的左、右焦点为
,
,点
,
,
为椭圆
上一动点,过点
的直线
交椭圆于
,
两点,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.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/8f5e0005baadf4e655c1b377487c8af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138bcbc42bc1c7230c4a325aee56153b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1badfc214fee86f3e31cbf5cd35090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.若![]() ![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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名校
3 . 已知双曲线
:
的左、右焦点为
,
,
为双曲线
渐近线上一点.满足
,且直线
,
的斜率之和为
,则双曲线
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce67f2138e7295cd72d66b2908cb6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/824a761a49c9ac1139d205f182bfc031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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|
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|
3卷引用:安徽省芜湖市2022-2023学年高三上学期期末数学试题
4 . 已知抛物线
:
的焦点为
,过焦点
的直线
与抛物线交于
,
两点,当直线
的倾斜角为
时,
.
(1)求抛物线
的方程;
(2)求证:过焦点
且垂直于
的直线与以
为直径的圆的交点分别在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311c73f960fc4b8f21402057d6150f50.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:过焦点
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-01-13更新
|
276次组卷
|
3卷引用:安徽省芜湖市2022-2023学年高三上学期期末数学试题
解题方法
5 . 五面体
中,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/17/410353fe-220b-4b60-8b28-c7dbaee37168.png?resizew=182)
(1)证明:
;
(2)给出①
;②
;③平面
平面
.
试从中选两个作为条件,剩下一个作为结论,可以让推理正确,请证明你的推理,并求出平面
和平面
夹角的余弦值.
注:如果选择不同组合分别解答,则按照第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1773fc257a6f487d80c422887dd56d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856e8dc5903774a95bd29dcc2c9877bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35112927cf711e1c9fa4c7dd392465b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f94ab32614c7ec18fd8a7549d712d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af21524a6664ab1321e8ee1d53277996.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/17/410353fe-220b-4b60-8b28-c7dbaee37168.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdd872d41982e7b50ed2aba66595f8d.png)
(2)给出①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e3f834d569575e10b7b7af40ff4548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff113d0df4877b8877721b05afb0321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5352d28609d1b3d09a0a29d023d1bb72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61510c34c5795d7261569b4d09098271.png)
试从中选两个作为条件,剩下一个作为结论,可以让推理正确,请证明你的推理,并求出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebce46aeb97373353179e5669365fa4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
注:如果选择不同组合分别解答,则按照第一个解答计分.
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6 . 如图,在四棱锥
中,
,
,
,
平面
,
,
为线段
上一点且
.
∥平面
;
(2)若
,二面角
的正弦值为
,求PD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4794f2d40733122dbf35a7dd6cf96131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6569c61bfa235b6a13a80cc4dbf4706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64785e4401e1d79632e360fd3626ed62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
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名校
解题方法
7 . 椭圆
的上下顶点分别
,焦点为
,
为椭圆上异于
的一动点,离心率为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef404abca1f78da130a38849f58559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
A.![]() ![]() |
B.离心率![]() ![]() ![]() |
C.直线![]() ![]() |
D.存在点![]() ![]() ![]() |
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2023-01-11更新
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1501次组卷
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4卷引用:安徽省六安市省示范高中2022-2023学年高三上学期期末数学试题
安徽省六安市省示范高中2022-2023学年高三上学期期末数学试题(已下线)专题21 解析几何中的定点与定值问题福建省福州第四中学2022-2023学年高二下学期开学考数学试题(已下线)模块四 专题6 暑期结束综合检测6(能力卷)(人教B)
8 . 已知两点
、
,动点M满足直线MA与直线MB的斜率之积为3.,动点M的轨迹为曲线C.
(1)求曲线C的方程;
(2)过点
作直线
交曲线C于P、Q两点,且两点均在y轴的右侧,直线AP、BQ的斜率分别为
、
.
①证明:
为定值;
②若点Q关于x轴的对称点成点H,探究:是否存在直线l,使得
的面积为
,若存在,求出直线l的方程,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
(1)求曲线C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
②若点Q关于x轴的对称点成点H,探究:是否存在直线l,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21871e06601d895874b1b8a49b1b808f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0874f019492261eb175bdcc08c189d.png)
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2023-01-11更新
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4卷引用:安徽省六安市省示范高中2022-2023学年高三上学期期末数学试题
安徽省六安市省示范高中2022-2023学年高三上学期期末数学试题(已下线)安徽省“江南十校”2023届高三下学期3月一模数学试题变式题17-222.2双曲线 测试卷-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册专题04 双曲线15种常见考法归类(3)
解题方法
9 . 设动直线
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4301c0f746b050d0445f1eec21c754bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027830fc47290062692964077ee481e4.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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10 . 一种糖果的包装纸由一个边长为6的正方形和2个等腰直角三角形组成(如图1),沿AD,BC将2个三角形折起到与平面ABCD垂直(如图2),连接EF,AE,CF,若G为FC上的动点,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/10/bd7e0fb4-7044-4673-8d19-860dca52bc3b.png?resizew=496)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/10/bd7e0fb4-7044-4673-8d19-860dca52bc3b.png?resizew=496)
A.若G为线段FC的中点,则![]() |
B.多面体ABCDFE的体积为144 |
C.![]() |
D.![]() |
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