真题
1 . 设
是二次曲线C上的点,且
构成了一个公差为
的等差数列,其中O是坐标原点.记
.
(1)若C的方程为
.点
及
,求点
的坐标;(只需写出一个)
(2)若C的方程为
.点
,对于给定的自然数n,证明:
成等差数列;
(3)若C的方程为
,点
,对于给定的自然数n,当公差d变化时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d38cb28701863eeeb21c28509ca10a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed981413b4dbc2becc7e18e0422858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2398f658821ecd05f7cb1c6a286fda0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2efba990f1fca3fe00fb5e0a7fff0bf0.png)
(1)若C的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc16c41b0d1e74725769b22b76a8d1b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac154c5d5230bc411f1f40ae5ee2ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f42d47ea24091b93e1aae372abf4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)若C的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749234eaf0dd6d14f6f538a81f62587c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f80b9e5603c903c73823aa9845906b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c09c5f86ca80a08f64eb04e3213dfd.png)
(3)若C的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d83c1c494a901e6a225b1f36ad334c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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