在直角坐标系xOy中,
是以PF为底边的等腰三角形,PA平行于x轴,点
,且点P在直线
上运动.记点A的轨迹为C.
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498163982155776/2500057368576000/STEM/e3d6f6f1a6d34e27a061f269b88a4d30.png?resizew=231)
(1)求C的方程.
(2)直线AF与C的另一个交点为B,等腰
底边的中线与直线
的交点为Q,试问
的面积是否存在最小值?若存在,求出该值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498163982155776/2500057368576000/STEM/e3d6f6f1a6d34e27a061f269b88a4d30.png?resizew=231)
(1)求C的方程.
(2)直线AF与C的另一个交点为B,等腰
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
更新时间:2020-07-06 14:42:38
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解题方法
【推荐1】已知点M到点
的距离比它到直线l:
的距离小
,记动点M的轨迹为E.
(1)求E的方程;
(2)若过点F的直线交E于
,
两点,则在x轴的正半轴上是否存在点P,使得PA,PB分别交E于另外两点C,D,且
?若存在,请求出P点坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0436039bcb24dab81c2664575dbad83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求E的方程;
(2)若过点F的直线交E于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbdff631fdfbd73e581bd7c38e1bbb7.png)
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名校
解题方法
【推荐2】在平面直角坐标系中,已知点
,直线
,动直线
垂直于
于点
,线段
的垂直平分线交
于点
,设
的轨迹为
.
(1)求曲线
的方程;
(2)以曲线
上的点
为切点作曲线
的切线
,设
分别与
,
轴交于
,
两点,且
恰与以定点
为圆心的圆相切. 当圆
的面积最小时,求
与
面积的比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b95463a97c60db3250cb641bf6523d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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)以曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a543f55354bcc4a637ed9198685eb7a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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【推荐1】已知以坐标原点
为圆心的圆与抛物线
:
相交于不同的两点
,与抛物线
的准线相交于不同的两点
,且
.求抛物线
的方程;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c885c8ea4baa8dcdc1bb3f8519104f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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【推荐2】已知抛物线C的顶点为原点,焦点F与圆
的圆心重合.
(1)求抛物线C的标准方程;
(2)设定点
,当P点在C上何处时,
的值最小,并求最小值及点P的坐标;
(3)若弦
过焦点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd767240a603ca0c0db5567707eb704.png)
(1)求抛物线C的标准方程;
(2)设定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8042f1b6b556402ac07fc69d92e21924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2777de400b45fee1fb1262544d3fbcb.png)
(3)若弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5457baa379234afd6db167db272bf5d0.png)
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解题方法
【推荐1】已知抛物线
,点
,斜率为
的直线l过点P,与E相交于不同的点A,B.
(1)求k的取值范围;
(2)斜率为
的直线m过点P,与E相交于不同的点C,D,证明:直线
,直线
及y轴围成等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84107fc934c3519b7f9c0121506801c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57f41842628a2f1138a9f0e7939fb20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
(1)求k的取值范围;
(2)斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fc303cfac1c7534451fb0789e68340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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解题方法
【推荐2】抛物线
上恒有两点关于直线
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0261104a7c308433a0c0508ff20ea29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92bd17a617425409cd4ff7b587f9bb3.png)
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