1 . 已知双曲线
:
(
,
)的右顶点
,斜率为1的直线交
于
、
两点,且
中点
.
(1)求双曲线
的方程;
(2)证明:
为直角三角形;
(3)若过曲线
上一点
作直线与两条渐近线相交,交点为
,
,且分别在第一象限和第四象限,若
,
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a62c9695f5a1691c5fe8724fa764b7.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef6fe3679e4dc29469edbccc75a682b.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d2db60d829a21a33490b2fed366546.png)
(3)若过曲线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184459410405a907798a625760c0d717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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2024-03-01更新
|
2352次组卷
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4卷引用:黑龙江省牡丹江市第二高级中学2024届高三下学期高考考前热身卷(一)数学试题
2 . 在平面直角坐标系
中,双曲线
的实轴长为4,渐近线方程为
.
(1)求双曲线H的标准方程;
(2)过点
作直线
交双曲线H左右两支于
两点(异于顶点),点A关于x轴的对称点为E,证明直线
过定点Q;
(3)过双曲线H上任意不同的两点
分别作双曲线H的切线,若两条切线相交于点M,且
,在第(2)的条件下,求
的最大值及此时点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5063b9c128dc6dcfa9cd3932b8446faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e229870f126b31e37965bc0c58667.png)
(1)求双曲线H的标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c153027427477bcd0a7228b14ce96cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(3)过双曲线H上任意不同的两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a819f5b20a0daa629b7dad124482cc0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f10f9679275de120c872be4fdbf69c.png)
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解题方法
3 . 如图1,在平行四边形
中,
,将
沿
折起,使点D到达点P位置,且
,连接
得三棱锥
,如图2.
平面
;
(2)在线段
上是否存在点M,使平面
与平面
的夹角的余弦值为
,若存在,求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20410a661bef707edc4bde87dea084c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307d38cc7012c328f1f22aa793fe76d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176385d91d5e29324fce4a932eff6a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6503ca085e3ca5f2ba723b0dd66e210b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450aa785fe5021ea99abb8f496293f5a.png)
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2024-02-27更新
|
2476次组卷
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4卷引用:黑龙江省哈尔滨市第三中学校2024届高三学年第一次模拟考试数学试卷
黑龙江省哈尔滨市第三中学校2024届高三学年第一次模拟考试数学试卷(已下线)期中考试押题卷(考试范围:第6-7章)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)广东省梅州市兴宁市第一中学2023-2024学年高二下学期月考一(3月)数学试题(已下线)专题01 空间向量与立体几何解答题必考题型(6类题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(江苏专用)
4 . 如图1,在平面四边形
中,
,
.点
是线段
上靠近
端的三等分点,将
沿
折成四棱锥
,且
,连接
,如图2.
平面
;
(2)求图2中,直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b1b3e2b758832c171d84722e2b5b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5623fbd0225a292c0160f384b1ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36aae82d53f2a35d2f95f467bd5b76cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbddb854a1a634484936c64ab4a9102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f8cd87144a823ca72d3917ffe55006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求图2中,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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2024-02-24更新
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2148次组卷
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4卷引用:黑龙江省齐齐哈尔市2024届高三第一次模拟考试数学试题
黑龙江省齐齐哈尔市2024届高三第一次模拟考试数学试题(已下线)第一套 艺体生新高考全真模拟 (一模重组卷)(已下线)专题04 立体几何四川省成都市金牛区实外高级中学2023-2024学年高二下学期第一阶段考试数学试题
名校
5 . 已知抛物线
(
)的准线为l,过抛物线上一点B向x轴作垂线,垂足恰好为抛物线C的焦点F,且
.
(1)求抛物线C的方程;
(2)设l与x轴的交点为A,过x轴上的一个定点
的直线m与抛物线C交于D,E两点.记直线
,
的斜率分别为
,若
,求直线m的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a4b3bddd48155c1e3eec7a8aea61588.png)
(1)求抛物线C的方程;
(2)设l与x轴的交点为A,过x轴上的一个定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7021efec959ee7f8c0405599e119b5.png)
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6 . 如图,在平面直角坐标系
中,抛物线C:
(
)与圆O的一个交点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/9/b568a608-559b-431b-9fc2-3fdd574b5c36.png?resizew=147)
(1)求抛物线C及圆O的方程;
(2)设直线l与圆O相切于点R,与抛物线C交于A,R两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20624370f8310a2da2f4e99f8f5a770.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/9/b568a608-559b-431b-9fc2-3fdd574b5c36.png?resizew=147)
(1)求抛物线C及圆O的方程;
(2)设直线l与圆O相切于点R,与抛物线C交于A,R两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b7fdcd237d89fd82b977ed60655ed2.png)
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解题方法
7 . 已知点A,B分别为椭圆E:(
)的左、右顶点,点
,直线BP交E于点Q,
,且
是等腰直角三角形.
(1)求椭圆E的方程;
(2)设过点P的动直线l与E相交于M,N两点,当坐标原点O位于以MN为直径的圆外时,求直线l斜率的取值范围.
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8 . 图1是直角梯形
,
,
,
,
,
,
在线段
上,且
,以
为折痕将
折起,使点
到达
的位置,且
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a63bd07c-aa38-4ebd-bc44-753a89833533.png?resizew=326)
(1)求证:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
(2)在棱
上存在点
,使得锐二面角
的大小为
,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a14895e4d42943e5a87ba078dd8268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2feceb4322d1f4627e0558c1a81743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fa3aea72ccc36948a4a90f7368f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9723635d46664a92d3af26362dfea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c8e857d113bd838fed693e584707a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297f713ddbcc4578e73c8afe3a52abfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9b02a4ece39842989088e56b1d988b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a63bd07c-aa38-4ebd-bc44-753a89833533.png?resizew=326)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570723ec1803bb3a69f220ad7df50226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f615c1e601990cde607f0216f715d57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
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2024-01-30更新
|
1371次组卷
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3卷引用:黑龙江省齐齐哈尔市2023-2024学年高二上学期期末考试数学试题
解题方法
9 . 已知抛物线
的焦点
到准线的距离为2.
(1)求抛物线
的方程;
(2)
为
上异于原点
的两点,以
为直径的圆过焦点
,求
最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c667eea919b8a084b02b4e786f07dde.png)
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解题方法
10 . 已知椭圆
:
左右焦点分别为
,
,离心率为
,
为
上的两个动点,且
面积的最大值为2.
(1)求
的方程.
(2)若
,
两点的纵坐标的乘积大于
,
是椭圆的左右顶点,且
.证明:直线
过定点.
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0b5a36e596cbbe8ced6df8a9f81511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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