解题方法
1 . 已知双曲线
的实轴长为2,设
为
的右焦点,
为
的左顶点,过
的直线交
于A,B两点,当直线AB斜率不存在时,
的面积为9.
(1)求
的方程;
(2)当直线AB斜率存在且不为0时,连接TA,TB分别交直线
于P,Q两点,设
为线段PQ的中点,记直线AB,FM的斜率分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e30d5827f2120d997997e4e31ba17.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当直线AB斜率存在且不为0时,连接TA,TB分别交直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2 . 如图,过双曲线
右支上一点P作双曲线的切线l分别交两渐近线于A,B两点,交x轴于点D,
,
分别为双曲线的左、右焦点,O为坐标原点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/1f62b0ff-37d3-4e99-aa23-5237deca3fdd.png?resizew=196)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eba4146208a9b519ee2cf649e733c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/1f62b0ff-37d3-4e99-aa23-5237deca3fdd.png?resizew=196)
A.![]() |
B.P为AB的中点 |
C.![]() ![]() |
D.若存在点P,使![]() ![]() |
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3 . 已知双曲线C:
与双曲线W:
的渐近线相同,且经过点
.
(1)求C的方程;
(2)已知C的上、下顶点分别为A,B,直线
与C交于不同的两点M,N,直线
与直线BM交于点G.证明:A,G,N三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29c0738fd840c1acadc91365ff366f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d34cf4ed961f4052ed35c7475c7d32e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b133e7d154c61264c8cda7355e4a97b0.png)
(1)求C的方程;
(2)已知C的上、下顶点分别为A,B,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65920f4695a14c85e7085450aee08b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca55362a9e187872cd20fa166f493b.png)
您最近一年使用:0次
2022-10-10更新
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512次组卷
|
2卷引用:黑龙江省齐齐哈尔市三立高级中学2022-2023学年高二上学期期中考试数学试题