1 . 在平面直角坐标系
中,以坐标原点O为极点,x轴的非负半轴为极轴建立极坐标系,直线l的极坐标方程为
,曲线C的参数方程为
(
为参数,
).
(1)求直线l的直角坐标方程及曲线C的普通方程;
(2)证明:直线l和曲线C相交,并求相交弦的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbfa74da8baf7a1a32f4d1fbb89cef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e006a66b83f3207ec4b3fd90ba9991f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb66f4db41478c23128adc14f2796556.png)
(1)求直线l的直角坐标方程及曲线C的普通方程;
(2)证明:直线l和曲线C相交,并求相交弦的长度.
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2018-10-12更新
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856次组卷
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3卷引用:【市级联考】山东省青岛市2019届高三9月期初调研检测数学(文)试题
2 . 已知椭圆
:
经过点
,离心率为
,点
为椭圆
的右顶点,直线
与椭圆相交于不同于点
的两个点
.
(1)求椭圆
的标准方程;
(2)当
时,求
面积的最大值;
(3)若
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e684712aade8dcebb62716843791034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455bae796d928c3c4d9090e924259628.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f55f82a88eb037a47971d8b3b9ca34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d67b5094972b896be121964f3b0be6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9e5716211c9f31e1cd910ccf352c95.png)
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