1 . 已知
为椭圆
上的点,对椭圆
上的任意两点P、Q,用如下办法定义它们的“和”
:过点S作一条平行于
(若点P与Q重合,则直线
表示椭圆
在P处的切线)的直线l与椭圆
交于不同于S的另一点,记作
(若l与椭圆
相切,则规定S为
).并规定
.
(1)若点
,求
、
以及
的坐标.
(2)在椭圆
上是否存在不同于S的点P,满足
?若存在,求出所有满足条件的点P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cacd4c2119a2381d627a45de68e2d263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459208d3062060f65fa347e6368e1457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460a3d908ee5647b7ba52c19740ef08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460a3d908ee5647b7ba52c19740ef08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460a3d908ee5647b7ba52c19740ef08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9eb1745e3e06d9a875107480c658b54.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc301000af55006ce42a131e6d56097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460a3d908ee5647b7ba52c19740ef08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1624d5e6bace3bfe3f7b69ddbd774a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ded53338ed7b2c20fd5e96522debbe4.png)
(2)在椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cb0ff741c5a50624b7fa1a0ddfc3b1.png)
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2 . 已知单位圆
上三个点
,
,
满足
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2499f2c837c79b4a3234304e7274b82.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e79718083af8cb21877878f9170142e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2499f2c837c79b4a3234304e7274b82.png)
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