解题方法
1 . 在平面直角坐标系
中,点M在x轴,y轴上的射影分别为A,B,直线MA,MB分别交直线
于D,E两点,且
与
的面积之和为1,记点M的轨迹为曲线C.
(1)求C的方程;
(2)P,Q两点在C上,
,求
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c204834608f1a8fba15747210dd7c5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372629a8666de1e9bac3e7daadcac7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022f0dc17db5fcc83b204dc845447ffc.png)
(1)求C的方程;
(2)P,Q两点在C上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ffe69ab39492e018a51e21b52dd0fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
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2 . 已知点
,直线
上有且仅有一点
满足
,则
可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7e26bd228679011198cf33e7b8bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a646ac0df52f1d728c8fe4659e6675c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e1bd05b71aa0f9f979b0d4cb543ae3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.0 | B.-1 | C.![]() | D.![]() |
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3 . 已知双曲线
,直线
与C交于A,B两点,点P是C上异于A,B的一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c4ed5a210e7f97bf194e37fd38ad8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
A.C的焦点到其渐近线的距离为![]() |
B.直线![]() ![]() |
C.过C的一个焦点作弦长为4的直线只有1条 |
D.点P到两条渐近线的距离之积为![]() |
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解题方法
4 . 已知双曲线
是关于
轴和
轴均对称的等轴双曲线,且经过点
.
(1)求
的方程;
(2)若
是
上一动点,直线
与
交于B,C两点,证明:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5bd206c0bafedf0212fa092bca6b28.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2de78b3148620cc740e52edb9a791c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dca1f769904e9fad2af78f7f526197c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
5 . 已知椭圆的焦点是椭圆
的顶点,椭圆
的焦点也是
的顶点.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654317ca05d25fee978869723ba8d0c8.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c5db73d81da5525d4d35885dac04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
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6 . 双曲线
的左、右焦点分别为
,
,
为
的右支上一点,分别以线段
,
为直径作圆
,圆
,线段
与圆
相交于点
,其中
为坐标原点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50dbcecd99fa41926a7bdbb75e8e556e.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/8a50ebd1b174cab382f6cbc82f92bf3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a455c83c7d8e4f9a91340eab24896e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() |
B.![]() |
C.点![]() ![]() ![]() |
D.圆![]() ![]() ![]() |
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2024-02-14更新
|
875次组卷
|
4卷引用:专题07 直线与圆、圆锥曲线
7 . 已知
是不共面的空间向量,若
与
(
是实数)是平行向量,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcca8dae02eab79376f1f775bcaa787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bf0952ffe99a5ce5e09c8d110bde0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c687be61ea8afa6c45e2165c305a76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
A.16 | B.-13 | C.3 | D.-3 |
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8 .
为椭圆
上一动点.
(1)结论一:动点M与定点
的距离和M到定直线
的距离的比为定值;
结论二:动点M与定点
的距离和M到定直线
的距离的比为定值;
从以上两结论中任选一个进行证明;
(2)过点
且斜率为正值的直线
交C于点A,过
且与
垂直的直线
与曲线C交于点B,当四边形
在x轴上方时,求其面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
(1)结论一:动点M与定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
结论二:动点M与定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
从以上两结论中任选一个进行证明;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ef6f0e1585b02d72fa399ce262f915.png)
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解题方法
9 . 已知向量
,
,则下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ee14381e00c9b46c39d4de41f28d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900b5631dd0aa30d9f8a3a73e87bc04.png)
A.向量![]() ![]() |
B.向量![]() ![]() ![]() |
C.若两个不同的平面![]() ![]() ![]() |
D.若平面![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
10 . 已知曲线
的左、右焦点分别为
,倾斜角为
的直线
经过左焦点
.直线
与曲线
的交点为
(
在
轴上方),过点
作
的平分线
的垂线,垂足为
为坐标原点.
(1)若
,求
内切圆的圆心
的横坐标和
的长;
(2)若
,求
的面积和
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab65b3e3f2e925c7073b83c4a74ef5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8255e035cfd3c2e84f10b236b6fd97.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3531f6214f5f5a46c8e755b6d14597f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3354a200890e00ef01b15a35a44b47e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
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2024-01-30更新
|
340次组卷
|
3卷引用:河北省邯郸市2023-2024学年高二上学期期末质量检测数学试题