名校
解题方法
1 . 已知是离心率为
的椭圆
:
(
)上任意一点,
是椭圆
的右焦点,且
的最小值是1.
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](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/c5db41a1f31d6baee7c69990811edb9f.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/9f2e70ea9dca32e6f14ae26be4431457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-01-13更新
|
460次组卷
|
3卷引用:黑龙江省哈尔滨市六校2023-2024学年高二上学期1月期末联考数学试题
2 . 已知椭圆
:
的左、右焦点分别是
,
,上顶点为
,椭圆的焦距等于椭圆的短轴长,且
的面积为1.
(1)求椭圆
的方程;
(2)若动直线
:
交椭圆于
,
两点,在
轴上是否存在定点
,使
?若存在,求出点
的坐标和
面积的最大值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dea9fd181099e4fab7a9c4b6149be32.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366cc36bccc0021d6c2ebdde697e3856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
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3 . 椭圆与双曲线
有相同的焦点,且过点
.
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图所示,记椭圆的左、右顶点分别为A,B,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(i)证明:点B在以为直径的圆内;
(ii)求四边形面积的最大值.
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名校
4 . 如图,在三棱柱
中,
,顶点
在底面
上的射影恰为点
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/5e0f8981-bd0e-481a-aa78-7e2d6358f3cb.png?resizew=177)
(1)证明:
平面
;
(2)
是线段
中点,求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d76cef03e6b2d02024495a840ab451.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/5e0f8981-bd0e-481a-aa78-7e2d6358f3cb.png?resizew=177)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c401f9dd333b36433b56d7aef1ffc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e367b683581c7cbe018078168f69efc5.png)
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名校
解题方法
5 . 如图,矩形
中
为边
的中点,将
沿直线
翻折成
,使
,若
为线段
的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/599a3b3e-4d98-4b40-a343-500f0080a1f0.png?resizew=187)
(1)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)求证:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(3)求二面角
夹角的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7a909494a000db960624410c5eee24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642e15f06c38176c827db801333153d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/599a3b3e-4d98-4b40-a343-500f0080a1f0.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f369bec2d5682bf6b8b317a08aff546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3e7c7845a0ec3cbac709fda131764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db26c5df2acdf210f3426fad185b1c20.png)
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2024·全国·模拟预测
名校
6 . 已知椭圆
,直线
过
的左顶点与上顶点,且
与两坐标轴围成的三角形的面积为1.
(1)求椭圆
的标准方程;
(2)已知点
,
(异于点
)是椭圆
上不同的两点,且
,过
作
的垂线,垂足为
,求
到直线
的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f5a1b728f09252ab59c246344267de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7ecb124fbef5522f7b65665578f0af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
7 . 如图,在四棱锥
中,
,
.
(1)求证:平面
平面
;
(2)若线段
上存在点
,满足
,且平面
与平面
的夹角的余弦值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22492d4603a55505b04ca8c2b1a0bba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8e49d68afab33806a63d25a0861c7c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/18dff587-0c9d-4bea-aa08-7aeaf7e4d539.png?resizew=160)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49677b8fcb3a9f400ac7707d30506d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e106f4233be16e98f2c1bf9f1635622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa3d53100990d378dfdf532184ee1fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-03更新
|
2006次组卷
|
4卷引用:黑龙江省哈尔滨市第三中学2024届高三上学期期末数学试题
名校
解题方法
8 . 已知椭圆
的左、右顶点为
,点
是椭圆
的上顶点,直线
与圆
相切,且椭圆
的离心率为
.
(1)求椭圆
的标准方程;
(2)过椭圆
右焦点
的直线
(与
轴不重合)与椭圆
交于
两点,若点
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f88df3ed2a92ccf774fee527d5a8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c16f562654c7b3102df1212dd653707e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dba6ef0c00b3442464e6d0f39cf5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60097cec26b613837579cff70a863a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-03更新
|
1036次组卷
|
5卷引用:黑龙江省哈尔滨市第三中学2024届高三上学期期末数学试题
黑龙江省哈尔滨市第三中学2024届高三上学期期末数学试题(已下线)每日一题 第19题 几何条件 坐标表示(高二)(已下线)专题27 直线与椭圆的位置关系及椭圆的弦长问题、面积问题(期末大题1)2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)(已下线)专题11椭圆(3个知识点7个拓展2个突破7种题型2个易错点)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)(已下线)2024年高考数学二轮复习测试卷(新高考Ⅱ卷专用)
9 . 如图,边长为4的两个正三角形
,
所在平面互相垂直,E,F分别为
,
的中点,点G在棱
上,
,直线
与平面
相交于点H.
(1)从下面两个结论中选一个证明:
①
;②直线
,
,
相交于一点;
注:若两个问题均作答,则按第一个计分.
(2)求点A到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a100d3638f0f04db2bd262c051f59b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(1)从下面两个结论中选一个证明:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3b9d2567109d0ff92a76f37afe47a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a16f5621716bfef7a056a3f2712feb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
注:若两个问题均作答,则按第一个计分.
(2)求点A到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b6917095bea8efd3154b72d737f013.png)
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10 . 已知
,
,平面内动点P满足
.
(1)求动点P的轨迹C的方程;
(2)动直线
交C于A、B两点,O为坐标原点,直线
和
的倾斜角分别为
和
,若
,求证直线
过定点,并求出该定点坐标;
(3)设(2)中定点为Q,记
与
的面积分别为
和
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d195911a91d12edd5685f6cd963fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743eac5ef7cd9452d9678d797da748ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb18941b1e55e62e6c3f54a35ccb214.png)
(1)求动点P的轨迹C的方程;
(2)动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f478abeeb4da23121b652cf907972d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设(2)中定点为Q,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592f84fbbd939b954f52dc6b8c009b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51aab5c5e99207337fb64603887579c.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/884d40a97fd767e95f34f3b91ab8d84c.png)
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