解题方法
1 . 以O为原点,
所在的直线为x轴,建立直角坐标系.设
,点F的坐标为
,
,点G的坐标为
.
(1)求
关于t的函数
的表达式,判断函数
的单调性(不需要证明);
(2)设
的面积
,若以O为中心,F为焦点的椭圆经过点G,求当
取得最小值时椭圆的方程;
(3)在(2)的条件下,若点P的坐标为
,C、D是椭圆上的两点,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08493c1e001d85731cb4863ec38857fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b062ab7377b2a9b3e4c4df0d3297cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fffad27b195220d9b31db743cd44eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94f384cef0393af2e36599c51b90548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992493990b269fd99c5393052813f6a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9fbbd668087e4811900a20e470d9bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa441e9ba1f9b8e145e0324244e5f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4301c9b8d06efd83eea4dfce15ec507.png)
(3)在(2)的条件下,若点P的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2957bcb77692d884e496df41499bca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b759a069dc3559f5f23c1dfda55cd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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