1 . 已知点
,
,
和动点
满足
是
,
的等差中项.
(1)求
点的轨迹方程;
(2)设
点的轨迹为曲线
按向量
平移后得到曲线
,曲线
上不同的两点M,N的连线交
轴于点
,如果
(
为坐标原点)为锐角,求实数
的取值范围;
(3)在(2)的条件下,如果
时,曲线
在点
和
处的切线的交点为
,求证:
在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b54b9cf95418bc3dce6e4c698b9907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3752eaf8b6f65d3faf930dc54bf2ef1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a476588acbf41d798cc234a52fa21a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7aaa871ceb78e5b80b531a7cf4f1c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22bd33096120ddae671fb7952f3f534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a981fb29b651cfdbd60c30b9781773c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在(2)的条件下,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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2 . 如图,在平面直角坐标系
中,已知函数
的图象为曲线
,点
在
上,点
在
轴上,且
分别是以
为直角顶点的等腰直角三角形.记点
的横坐标分别为
,
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/63b37273-c9ae-4227-87a1-1f6fbccbe7d5.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edeed0665fc1a8e99ceb7911fe137390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f36925a6e79016bbbf8c9cd77c3204e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee76826aa0f752c670dec0b6e2c21f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd7c9e9e534c62a758262894611823d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f36925a6e79016bbbf8c9cd77c3204e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93598e7e1512f621ce42ae2632d744c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242922097b33a636ca6210765ebca24e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/63b37273-c9ae-4227-87a1-1f6fbccbe7d5.png?resizew=168)
A.![]() | B.![]() |
C.![]() | D.![]() |
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