(Ⅰ)因为
![](https://iknow-pic.cdn.bcebos.com/d1160924ab18972baaf96a79e5cd7b899f510a45?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,即
![](https://iknow-pic.cdn.bcebos.com/0824ab18972bd4074a04b94e78899e510eb30945?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,
所以抛物线C的方程为
![](https://iknow-pic.cdn.bcebos.com/b21c8701a18b87d69553feac040828381f30fd74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
………-------------------------- 2分
设⊙M的半径为
![](https://iknow-pic.cdn.bcebos.com/86d6277f9e2f07089d147fb3ea24b899a901f274?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,则
![](https://iknow-pic.cdn.bcebos.com/7a899e510fb30f24c75986b0cb95d143ac4b0345?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,
所以
![](https://iknow-pic.cdn.bcebos.com/9f2f070828381f305e08d81aaa014c086e06f074?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
的方程为
![](https://iknow-pic.cdn.bcebos.com/9f510fb30f2442a75fcd9716d243ad4bd0130245?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
……………… 4分
(Ⅱ)
![](https://iknow-pic.cdn.bcebos.com/29381f30e924b899102d2c8b6d061d950a7bf674?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,设
![](https://iknow-pic.cdn.bcebos.com/0eb30f2442a7d9334f6b8ec0ae4bd11372f00145?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,
(1)当
![](https://iknow-pic.cdn.bcebos.com/d043ad4bd11373f00efc052ca70f4bfbfaed0445?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
斜率不存在时,
![](https://iknow-pic.cdn.bcebos.com/43a7d933c895d14324b58e9070f082025baf0745?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,则
![](https://iknow-pic.cdn.bcebos.com/09fa513d269759eeed413578b1fb43166d22df74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
--------6分
(2)当
![](https://iknow-pic.cdn.bcebos.com/d043ad4bd11373f00efc052ca70f4bfbfaed0445?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
斜率存在时,设PQ的方程为
![](https://iknow-pic.cdn.bcebos.com/ac4bd11373f08202d751fb8c48fbfbedaa641b45?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,
则
![](https://iknow-pic.cdn.bcebos.com/d01373f082025aaf2af11478f8edab64024f1a45?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
消
![](https://iknow-pic.cdn.bcebos.com/1c950a7b02087bf4cafd025af1d3572c11dfcf74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
得,
![](https://iknow-pic.cdn.bcebos.com/0b7b02087bf40ad1a3f59250542c11dfa9ecce74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,
所以
![](https://iknow-pic.cdn.bcebos.com/72f082025aafa40fc405a46ea864034f79f01945?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,-------------------------------------------8分
由因为
![](https://iknow-pic.cdn.bcebos.com/4afbfbedab64034feb0ea8b5acc379310b551d45?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,所以
![](https://iknow-pic.cdn.bcebos.com/622762d0f703918f6bc06879523d269759eec474?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,故
![](https://iknow-pic.cdn.bcebos.com/f603918fa0ec08fa9c1146145aee3d6d55fbda74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
。--------------------10分
所以
所以
![](https://iknow-pic.cdn.bcebos.com/f703738da977391215e5efd2fb198618377ae246?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
。-------------------------------------------------12分
20解:(Ⅰ)
当
![](https://iknow-pic.cdn.bcebos.com/3812b31bb051f8192fe669f9d9b44aed2f73e746?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
时,
![](https://iknow-pic.cdn.bcebos.com/3c6d55fbb2fb4316b90e2fc923a4462309f7d374?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
……………………2分
![](https://iknow-pic.cdn.bcebos.com/b21bb051f81986189c84853749ed2e738ad4e646?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
定义域:
![](https://iknow-pic.cdn.bcebos.com/42166d224f4a20a4910f697493529822720ed074?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
……………………4分
(Ⅱ)
![](https://iknow-pic.cdn.bcebos.com/4e4a20a4462309f7497ef8a1710e0cf3d7cad674?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
……………………5分
讨论:若
![](https://iknow-pic.cdn.bcebos.com/4bed2e738bd4b31c37fffe0884d6277f9f2ff846?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,即
![](https://iknow-pic.cdn.bcebos.com/08f790529822720ed0dfb74978cb0a46f21fab74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
时……………………6分
![](https://iknow-pic.cdn.bcebos.com/a8014c086e061d95b4855d8b78f40ad163d9ca46?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
在
![](https://iknow-pic.cdn.bcebos.com/0df3d7ca7bcb0a461233de8a6863f6246b60af74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
单调递增,在
![](https://iknow-pic.cdn.bcebos.com/d6ca7bcb0a46f21f5f250be0f5246b600c33ae74?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
上单调递减.
所以
![](https://iknow-pic.cdn.bcebos.com/267f9e2f07082838a8ceb6a7bb99a9014d08f146?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
……………………………8分
若
![](https://iknow-pic.cdn.bcebos.com/9f2f070828381f3051dae71aaa014c086f06f046?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
,即
![](https://iknow-pic.cdn.bcebos.com/060828381f30e9240167f6824f086e061c95f746?x-bce-process=image/resize,m_lfit,w_600,h_800,limit_1)
时………………………………9分