名校
解题方法
1 . 已知椭圆
的左焦点
,点
在椭圆
上,过点
的两条直线
分别与椭圆
交于另一点
,且直线
的斜率满足
.
(1)求椭圆
的方程;
(2)证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63587f0178ca6f60d893e2e29d231a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d059a0d71bddb677c603d84fac444b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86d920459c8efe08d73807772a0efc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8b196ae90f5bb109698dd7bcfc510f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2024-05-11更新
|
1256次组卷
|
5卷引用:新疆喀什地区2023-2024学年高三下学期4月适应性检测数学试题
新疆喀什地区2023-2024学年高三下学期4月适应性检测数学试题(已下线)数学(江苏专用03) 天津市第四十七中学2023-2024学年高二下学期5月期中数学试题(已下线)2024年高考全国甲卷数学(文)真题平行卷(基础)(已下线)2024年高考全国甲卷数学(理)真题变式题16-23
2024·全国·模拟预测
2 . 已知曲线
与曲线
关于直线
对称.
(1)求曲线
的方程.
(2)若过原点的两条直线分别交曲线
于点
,
,
,
,且
(
为坐标原点),则四边形
的面积是否为定值?若为定值,求四边形
的面积;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e0ccc4f4ffe46bf62e5ad2f48d89b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512f4c29ff276b7f35052ad4cc255ab5.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若过原点的两条直线分别交曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3507c9b7e478a3646b71934771a59d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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3 . 如图,在四棱锥
中,底面
为等腰梯形,
,且平面
平面
为
的中点.
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15728316d0626e5fbf897eb6343c7c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83511375ec2780ceb9ac603420249ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
您最近一年使用:0次
4 . “蒙旦圆”涉及的是几何学中的一个著名定理,该定理的内容为:椭圆上两条互相垂直的切线的交点必在一个与椭圆同心的圆上,该圆称为原椭圆的蒙日圆.若椭圆
的离心率为
,则该椭圆的蒙日圆方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8724f1a35b3bb3a91e45d2b235f0b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
您最近一年使用:0次
2024·新疆·二模
名校
解题方法
5 . 在斜三棱柱
中,
是边长为2的正三角形,侧面
底面
.
;
(2)
为
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9227c4e4503a97f1d469620a8bd74f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e5dc81fbafbe58bff0842f7776d80a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
您最近一年使用:0次
2024-04-15更新
|
835次组卷
|
3卷引用:新疆部分地区2024届高三高考素养调研第二次模拟考试数学试题
(已下线)新疆部分地区2024届高三高考素养调研第二次模拟考试数学试题2024届新疆维吾尔自治区塔城地区高三第二次模拟考试数学试题云南省昆明市第十四中学2023-2024学年高二下学期4月月考数学试卷
名校
6 . 如图,在四棱锥
中,底面
是边长为
的正方形.
是平面
和平面
的交线,证明:
;
(2)若四棱锥
的体积为
,二面角
和二面角
都是
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24caeb80a748bcbc9dc33cd430a5aca.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-04-15更新
|
883次组卷
|
3卷引用:新疆石河子第一中学2024届高三“天使计划”第二轮测试数学试题
7 . 抛物线
过点
,则焦点坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86022205a7487439dd8d0897cd3bf19.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-15更新
|
1027次组卷
|
3卷引用:新疆乌鲁木齐地区2024届高三第二次质量监测数学试题
8 . 已知抛物线
的焦点为
为抛物线
上的任意三点(异于坐标原点
),
,且
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2786fda111d2f8efcb6dc58aa0cbe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba11c7099e4fd590723a0e22aa4bfce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13f9134b42ec02fb4f1290279d0781f.png)
A.![]() |
B.若![]() ![]() |
C.设![]() ![]() ![]() ![]() |
D.若直线![]() ![]() ![]() |
您最近一年使用:0次
2024-04-13更新
|
1131次组卷
|
3卷引用:新疆石河子第一中学2024届高三“天使计划”第二轮测试数学试题
名校
9 . 设等差数列
的公差为
,则“
”是“
为递增数列”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abdf96d28023f6fe0f492e2bca2df8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8927e6db7dc997cc59ddb0ff5900c36.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充分必要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-04-08更新
|
2844次组卷
|
7卷引用:新疆石河子第一中学2024届高三“天使计划”第二轮测试数学试题
名校
解题方法
10 . 已知点
在抛物线
上,抛物线
的准线与
轴交于点
,线段
的中点
也在抛物线
上,抛物线
的焦点为
,则线段
的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f954a8da05cc9144d4bf86f88e236a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2024-04-07更新
|
1267次组卷
|
6卷引用:新疆石河子第一中学2024届高三“天使计划”第二轮测试数学试题
新疆石河子第一中学2024届高三“天使计划”第二轮测试数学试题陕西省商洛市2024届高三第四次模拟检测数学(文科)试题陕西省商洛市2024届高三第四次模拟检测数学(理科)试题(已下线)数学(新高考卷01,新题型结构)(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题6-10黑龙江省哈尔滨市第二十四中学校2024届高三下学期第三次模拟测试数学试题