动圆P过点
,且与直线
相切,设动圆圆心
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点F的直线交曲线C于A,B两个不同的点,过点A,B分别作曲线C的切线,且二者相交于点M,若直线
的斜率为
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点F的直线交曲线C于A,B两个不同的点,过点A,B分别作曲线C的切线,且二者相交于点M,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
更新时间:2019-01-30 10:40:16
|
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解答题-证明题
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较难
(0.4)
名校
解题方法
【推荐1】已知动点P到定点
的距离比P点到直线
的距离小2,设动点P的轨迹为曲线C.过定点
的直线
与曲线C交于A、B两点.
(1)求曲线C的方程;
(2)若点E的坐标为
,求证:
;
(3)是否存在实数
,使得以
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:
所得弦长为定值?若存在,求出实数
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
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(1)求曲线C的方程;
(2)若点E的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc5d60d9de86ffde026415822c986ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053a900542a8c0c145734566cb4cf4ad.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解答题-问答题
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【推荐2】在平面直角坐标系
中,已知点
,点B在直线
上,点M满足
,
.点M的轨迹为曲线C.
(1)求曲线C的方程;
(2)点P在曲线C上,且横坐标为2,问:是否在曲线C上存在D,E两点,使得
是以P为直角顶点的等腰直角三角形?若存在,说明
的个数;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a2b8b43e1fe82fc439d145e91b860c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6e77458243a887e69f84565551cfe5.png)
(1)求曲线C的方程;
(2)点P在曲线C上,且横坐标为2,问:是否在曲线C上存在D,E两点,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d06fad1ed5a452a835e9a02cb011ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d06fad1ed5a452a835e9a02cb011ed2.png)
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解答题-问答题
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较难
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【推荐1】已知抛物线
上的动点M到直线
的距离比到抛物线E的焦点F的距离大
.
(1)求抛物线E的标准方程;
(2)设点Q是直线
上的任意一点,过点P(1,0)的直线l与抛物线E交于A、B两点,记直线AQ、BQ、PQ的斜率分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
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(1)求抛物线E的标准方程;
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5653be7a245e1c0c86b5fb82cf8e623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b0290f2518ed9a67a74bf3de66dfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f7e9d276e2fd336e3573af0434605e.png)
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【推荐2】已知抛物线
上横坐标为
的点
到焦点
的距离为
.
(I)求抛物线的方程;
(II)若斜率为
的直线
与抛物线
交于
两点,且点
在直线
的右上方,求证:△
的内心在直线
上;
(III)在(II)中,若
,求△
的内切圆半径长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(I)求抛物线的方程;
(II)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08e91d2fa9519a5f48d488176700499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
(III)在(II)中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71272f10d3f406389c53e73966934380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
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