平面直角坐标系中,动点M到定点
的距离与它到直线
的距离之比为
,
(1)求点M的轨迹方程.
(2)若点
,则求
的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0590d52d79cde257d810882f9e7bb403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae2ccaececa8674201e84bb4f7a4f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
(1)求点M的轨迹方程.
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e673c5aa17d19a2a9edb7b27a1ef2de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e6f7ef8ede7bce7c46ae6ecc5bfe54.png)
21-22高二上·山东威海·期中 查看更多[2]
更新时间:2021-12-25 22:56:40
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相似题推荐
解答题-问答题
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适中
(0.65)
名校
解题方法
【推荐1】已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e828c48d36b9ca11e2b44240b0eca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b926c36373d890b9b6180cd86b0a98.png)
(1)求
的轨迹![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过轨迹
上任意一点
作圆
的切线
,设直线
的斜率分别是
,试问在三个斜率都存在且不为0的条件下,
是否是定值,请说明理由,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e828c48d36b9ca11e2b44240b0eca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b926c36373d890b9b6180cd86b0a98.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56648a303009f944e1a9983c3f62c7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388737b5d38e8aa7bc8cfb1da4f9fc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e8419e2844b4061d07ce1df93859d3.png)
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【推荐2】已知
,
,且
的周长为
,记点
的轨迹为曲线
.直线
:
与曲线
交于不同两点
,
.
(1)求曲线
的方程;
(2)是否存在直线
使得
?若存在,求出直线
的方程,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e30645f36e8628b9e25d53598d5174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37df9dad3961893b22d6639c4311e267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafa8e628e4995e60cc3400028e900b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f556a4584fc8192d526a2bddfc9ccbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec34991f23c63afef8304444174e686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
【推荐1】在平面直角坐标系
中,已知椭圆
:
(
)的离心率
,且椭圆
上的点到点
的距离的最大值为3.求椭圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234e7679481ec0d01c915b7fbb71891d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75ebcf0d951f833ca90e040f3cd4db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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【推荐2】已知双曲线
:
的焦距为
,其中一条渐近线的方程为
.以双曲线
的实轴为长轴,虚轴为短轴的椭圆记为E,过原点О的动直线与椭圆E交于A,B两点.
(1)求椭圆E的方程;
(2)若点Р为椭圆E的左顶点,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5212f9b39ca710f0349e1b3652bc6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆E的方程;
(2)若点Р为椭圆E的左顶点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f73cf40dff3361e220600639155c1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599915425cf7454623e4e6fcff0413bc.png)
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