已知
,点B是
轴上的动点,过B作AB的垂线
交
轴于点Q,若
.
![](https://img.xkw.com/dksih/QBM/2013/4/19/1571189377703936/1571189383446528/STEM/58aada2443ee45c0b9f1e4d783785a0d.png?resizew=234)
(1)求点P的轨迹方程;
(2)是否存在定直线
,以PM为直径的圆与直线
的相交弦长为定值,若存在,求出定直线方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4532879711babba5dedf6bcea14a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117670fce6419cb0acf919486ef82e4c.png)
![](https://img.xkw.com/dksih/QBM/2013/4/19/1571189377703936/1571189383446528/STEM/58aada2443ee45c0b9f1e4d783785a0d.png?resizew=234)
(1)求点P的轨迹方程;
(2)是否存在定直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
2013·湖南长沙·一模 查看更多[2]
更新时间:2016-12-02 06:15:53
|
相似题推荐
解答题-问答题
|
适中
(0.65)
解题方法
【推荐1】已知椭圆
的短轴上端点为P,过点P作椭圆互相垂直的两弦
.连接
,试求点P在
上的射影Q的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc603fea876cbf85b1efcb5bab0d500f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解答题-问答题
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适中
(0.65)
名校
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【推荐2】如图,在平面直角坐标系中,已知点F(1,0),过直线l:x=4左侧的动点P作PH⊥l于点H,∠HPF的角平分线交x轴于点M,且|PH|=2|MF|,记动点P的轨迹为曲线C.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/519b7891-4229-4a0a-8cff-0c4240630901.png?resizew=284)
(1)求曲线C的方程;
(2)过点F作直线l′交曲线C于A,B两点,设
,若λ∈
,求|AB|的取值范围.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/519b7891-4229-4a0a-8cff-0c4240630901.png?resizew=284)
(1)求曲线C的方程;
(2)过点F作直线l′交曲线C于A,B两点,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97701a2f599401f400a604ae0c66d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b448fe164c2c2931805e3b3847dcdd75.png)
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解答题-问答题
|
适中
(0.65)
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解题方法
【推荐1】已知抛物线
,过点
作不与x轴垂直的直线
,
分别与抛物线C交于M,N和P、Q两点.
(1)若M,N两点的纵坐标之和为-6,求直线l的斜率;
(2)证明:
;
(3)若点E为线段MN的中点,点G为线段PQ的中点,求
的值.
注:k表示直线的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53efcba08b1c0c9f7b495c2a289ebea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
(1)若M,N两点的纵坐标之和为-6,求直线l的斜率;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c719342ee48eb3c22ae4c78f5e325e.png)
(3)若点E为线段MN的中点,点G为线段PQ的中点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0465c3a283ffcf2b26097c9a8e3d380.png)
注:k表示直线的斜率.
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【推荐2】如图,已知抛物线
的焦点为
,圆心为焦点的圆
与
轴相切.过
点的直线
交抛物线与圆分别为
(从上到下).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/9c3ff26f-02e6-4c4e-be3a-b035278b93a3.png?resizew=128)
(1)证明:
是定值;
(2)若
,
的面积比是
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20490cf9cedbd19be05c3ede9d80f504.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/9c3ff26f-02e6-4c4e-be3a-b035278b93a3.png?resizew=128)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba9fc9ae9bc7000a7f3daba16091a02.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbf9680f74a9ac5d934304654ce2771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4686f39b38d5b90309ee73ed89a0640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84783b6ba0f36789519816101a437f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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