11-12高二上·福建福州·期末
解题方法
1 . 设
分别是椭圆C:
的左右焦点,
(1)设椭圆C上的点
到
两点距离之和等于4,写出椭圆C的方程和焦点坐标.
(2)设K是(1)中所得椭圆上的动点,求线段
的中点B的轨迹方程.
(3)设点P是椭圆C 上的任意一点,过原点的直线L与椭圆相交于M,N两点,当直线PM ,PN的斜率都存在,并记为
试探究
的值是否与点P及直线L有关,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7192d60347d61806c20c12d689eea94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b70b84716263fce4fbfb07a452db5d.png)
(1)设椭圆C上的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f09608e82496b033260bbb23a9ef992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7192d60347d61806c20c12d689eea94.png)
(2)设K是(1)中所得椭圆上的动点,求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835e801412b215b81173a28b42f67b42.png)
(3)设点P是椭圆C 上的任意一点,过原点的直线L与椭圆相交于M,N两点,当直线PM ,PN的斜率都存在,并记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fc9902b2128b1b2e2c76ee2e3634cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee11bc715bdd98c730b1b791e922b30.png)
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11-12高三上·浙江嘉兴·阶段练习
名校
2 . 已知抛物线
的顶点在原点,焦点在
轴正半轴上,点
到其准线的距离等于
.
(Ⅰ)求抛物线
的方程;
(Ⅱ)如图,过抛物线
的焦点的直线从左到右依次与抛物线
及圆
交于
、
、
、
四点,试证明
为定值.
![](https://img.xkw.com/dksih/QBM/2011/11/9/1570346597523456/1570346603012096/STEM/f35dc38c08354d48926a00e9f905751b.png?resizew=201)
(Ⅲ)过
、
分别作抛物
的切线
、
,且
、
交于点
,求
与
面积之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c0980761f2c189bb51b9c12a79d77d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(Ⅰ)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(Ⅱ)如图,过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e318cefab1d71238b6a770e9d5fe154e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba9fc9ae9bc7000a7f3daba16091a02.png)
![](https://img.xkw.com/dksih/QBM/2011/11/9/1570346597523456/1570346603012096/STEM/f35dc38c08354d48926a00e9f905751b.png?resizew=201)
(Ⅲ)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0288f5a9e234c0fc858c89f0a30c003b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2640a7425ddd37334d14a5443479b3.png)
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