名校
1 . 如图(1),平面直角坐标系中,
的方程为
,
的方程为
,两圆内切于点
,动圆
与
外切,与
内切.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/c5c34261-7ad0-4368-9307-0a837e414a5c.png?resizew=197)
(1)求动圆
圆心
的轨迹方程;
(2)如图(2),过
点作
的两条切线
,若圆心在直线
上的
也同时与
相切,则称
为
的一个“反演圆”
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/2f99b74f-6788-499a-9a34-56f93f9d603b.png?resizew=262)
(ⅰ)当
时,求证:
的半径为定值;
(ⅱ)在(ⅰ)的条件下,已知
均与
外切,与
内切,且
的圆心为
,求证:若
的“反演圆”
相切,则
也相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6d5018b988d9843479cfdcfd3a522d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c72c070f4f4d2b44927391b59a1e755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afc954e87bd737ec051d5c94837c8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c72c070f4f4d2b44927391b59a1e755.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/c5c34261-7ad0-4368-9307-0a837e414a5c.png?resizew=197)
(1)求动圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)如图(2),过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29129b19694fa17794c0f84d41b4e6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1600fb87bca9e069b64fe30fcb90816a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1600fb87bca9e069b64fe30fcb90816a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/2f99b74f-6788-499a-9a34-56f93f9d603b.png?resizew=262)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc895959e9bc92294dc9dd2263dbf0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1600fb87bca9e069b64fe30fcb90816a.png)
(ⅱ)在(ⅰ)的条件下,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa00b7a23f7a9aadae6d22dcb28a705a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c72c070f4f4d2b44927391b59a1e755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4535f154616b014bd29db79d45c9f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa00b7a23f7a9aadae6d22dcb28a705a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a77bfa0ef5e5a1999649892e7b263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa00b7a23f7a9aadae6d22dcb28a705a.png)
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