1 . 教材曾有介绍:圆
上的点
处的切线方程为
我们将其结论推广:椭圆
的点
处的切线方程为
在解本题时可以直接应用,已知直线
与椭圆E:
有且只有一个公共点.
(1)求
的值;
(2)设O为坐标原点,过椭圆E上的两点A、B分别作该椭圆的两条切线
,且
与
交于点M![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf278d3ece654fea3fdf89e532c685a9.png)
①设
,直线AB、OM的斜率分别为
,求证:
为定值;
②设
,求△OAB面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27477c4eba717135b559c18fb786e36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f965cfee1311f0df39396b035770e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d891034f9d4ee622e083d44989b7fdc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27477c4eba717135b559c18fb786e36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65adcbe574b14ad635df2c6f03f4822f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c93215f460bffca5bdae786eb42144b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98f8484a21113a5e5b933ab1b0c9114.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设O为坐标原点,过椭圆E上的两点A、B分别作该椭圆的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.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/cf278d3ece654fea3fdf89e532c685a9.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
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