解题方法
1 . 已知
是椭圆
的两个焦点坐标,
是椭圆
上的一个定点,
是椭圆
上的两点,点
的坐标为
.
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968712640217088/2968854119260160/STEM/a4ed759b4dbb41a2a8d4a93242f32ef3.png?resizew=189)
(1)求椭圆
的方程;
(2)当
两点关于
轴对称,且
为等边三角形时,求
的长;
(3)当
两点不关于
轴对称时,证明:△
不可能为等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f393d91d36d6e54e8da54eb7df0429e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5795873a3546820b08ce85aadfe0222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968712640217088/2968854119260160/STEM/a4ed759b4dbb41a2a8d4a93242f32ef3.png?resizew=189)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726dafd729b858ae0c8b68c1c828b666.png)
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2 . 如图,已知椭圆
:
,过点
的直线
与椭圆
相切于第一象限的点
,
是坐标原点,
于
.
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716738541166592/2718703508905984/STEM/5536c385-1c4a-4786-b1ba-83a029b0ace7.png?resizew=306)
(1)求点
的坐标(用
表示):
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27179665507e05bad551e8a4d79d593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a933dd7affa1d7542c62449ab99f00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716738541166592/2718703508905984/STEM/5536c385-1c4a-4786-b1ba-83a029b0ace7.png?resizew=306)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0314bc045000a86dc0c7ae3a5d011fd9.png)
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3 . 如图,已知圆
和椭圆
,点
,
,直线
交
轴于
,直线
平行
轴交
于
(点
在
轴上方),
,直线
交
于点
,直线
交
轴于点
,则椭圆的长轴长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b96eda0601673fafb836643969914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11768d6756d082c8a8a2f1c84a83ff72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed75a38d78c05a6c5ceda8e5ba374cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752827aaf632e854c10f7814aff9a53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ad8115387158c8dda205d26968ba11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e884ca9429486026caa5e2310b0e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc46f09a8c079e2916af98bb2f96f84.png)
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