名校
解题方法
1 . 我们用“
”表示“将直角坐标平面内点
进行变换后得到
,即
,已知
,
,若存在一个圈,使所有的点
都在这个圆内或圆上,则称这个圆为
的一个收敛圈.
(1)若
,且
,判断
是否存在半径为
的收敛圆.并说明理由;
(2)若
,且
,求
的半径最小的收敛圆
的方程.
(3)对于(2)中的图
上一点
,
,
的轨迹为
,
,
分别是椭圆
的焦点,
是
上异于
,
的一点,直线
,
与
分别相交于点
、
和
、
,判断
是否为定值,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/313beecd55e2e5b85f228d6f0f5c3dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37eb0772312c457caf2ed453a3a58191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce71b5030a0300d1448068ae802f2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9972a83d919fd17f2b095d83d8845e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c051c2459ca7e2edd8ece9e565ec4b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c051c2459ca7e2edd8ece9e565ec4b09.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d601cbdab54426a600af00c1b7c8b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f05b989842734d1afd9429d15f5484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c051c2459ca7e2edd8ece9e565ec4b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f208a06ac596f9cb08545b092e2bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640a608518f7cffb5454249f4f915e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c051c2459ca7e2edd8ece9e565ec4b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
(3)对于(2)中的图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a29d02c206df39e77fb6d80c5acc4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b40ae9a2b5c2d3ff6c98c93e9fafc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c888eba416ceca9d0b82e8cae3017846.png)
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