1 . 已知双曲线
经过点
,且
的一条渐近线的方程为
.
(1)求
的标准方程;
(2)若点
是
的左顶点,
是
上与顶点不重合的动点,从下面两个条件中选一个,求直线
与
的斜率之积.
①
关于原点对称;②
关于
轴对称.
注:若选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1362c0809439106817fa2572994bb8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](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/fcc5dd4d07e2098d8d1b731f2622867f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
注:若选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2024-02-14更新
|
292次组卷
|
2卷引用:广东省河源市2023-2024学年高二上学期期末考试数学试题
名校
2 . 在平面内,动点
与定点
的距离和它到定直线
的距离比是常数3.
(1)求动点M的轨迹方程;
(2)若直线m与动点M的轨迹交于P,Q两点,且
(O为坐标原点),求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc45c2720dcd877ad04fc97c9862a50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2df7b8e045af97463654b0edb96390a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7810baa38678c7afa23010cb41efb0e8.png)
(1)求动点M的轨迹方程;
(2)若直线m与动点M的轨迹交于P,Q两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52cbc12fa97eca2aa53694bee31f3c07.png)
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解题方法
3 . 已知双曲线
为双曲线
上的任意点.
(1)求双曲线
的两条渐近线方程及渐近线夹角的大小;
(2)求证:点
到双曲线
的两条渐近线的距离的乘积是一个常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc8c2e80988e01d00354213b6ab9a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2024-02-12更新
|
214次组卷
|
3卷引用:上海市新川中学2023-2024学年高二上学期期末数学试题
上海市新川中学2023-2024学年高二上学期期末数学试题上海市嘉定区第二中学2023-2024学年高二下学期3月月考数学试题(已下线)专题04 圆锥曲线(六大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
4 . 已知双曲线
的上、下焦点分别是
,P为双曲线C上支上的动点,
.
(1)求双曲线C的方程;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01fdaad96da6a0008b23bb4230125e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4f7e7f33963df24d6a46067b4677e5.png)
(1)求双曲线C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7285470bf401f5edaac641234ee6ff6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe1cad1ce47339827ac5047af4647d.png)
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名校
解题方法
5 . 已知双曲线C和椭圆
有公共的焦点,且离心率为
.
(1)经过点
作直线l交椭圆交于A,B两点,且M为AB的中点,求直线l的方程.
(2)求双曲线C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97caea8ea20c118920d887d2ee9ac83d.png)
(2)求双曲线C的方程.
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6 . 已知等轴双曲线
的对称轴都在坐标轴上,并且经过点
,求双曲线
的标准方程、离心率、实轴长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6300e1ebe1e6b8ee9743e2da16f02f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
7 . 根据下列条件,分别求出曲线的标准方程:
(1)焦距是
,过点
,焦点在
轴上的椭圆;
(2)一个焦点是
,一条渐近线方程为
的双曲线;
(3)焦点到准线的距离是
,而且焦点在
轴上的抛物线.
(1)焦距是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b273241821170be56c5251d48386013b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)一个焦点是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3eda23a1350120ef959ae541d36657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b0e963195605a67975c6f8f3caa0c.png)
(3)焦点到准线的距离是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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解题方法
8 . 若双曲线
与
有相同的焦点,与双曲线
有相同渐近线.
(1)求双曲线
的标准方程;
(2)求过点
的抛物线标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f0fe85f726937cb3a0360a6681cf76.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a3619ccbcf65312754a970647014e5.png)
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解题方法
9 . 已知
是双曲线
上的一点,
分别是
的左、右焦点,若
.
(1)求双曲线
的离心率;
(2)当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222b4c3088d36ba0b2f5d8dedbcfc902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb16c92145df08bc3450b1484ead324e.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a3a52aaea364ffd886c735ffbdf0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
您最近一年使用:0次
名校
10 . 已知双曲线过点
且与椭圆
有相同的焦点
,
(1)求双曲线的标准方程;
(2)若点
在双曲线上,且
,求
与
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d95ab554e5ba1078cd4d40425171d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce7445cd0f42c7f88dc3efcb72c7969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48932773034bb6e1651acf140d47822c.png)
(1)求双曲线的标准方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4aaec620c8025f9bfe921aae8a04bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9795e5db34dcdc4d5af1eea3d433396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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