2014·福建福州·一模
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b45440b667c6cc4731c91c2011e0f98.png)
为自然对数的底数).
(1)求曲线
在
处的切线方程;
(2)若
是
的一个极值点,且点
,
满足条件:
.
(ⅰ)求
的值;
(ⅱ)若点
,判断
三点是否可以构成直角三角形?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b45440b667c6cc4731c91c2011e0f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e8d9500cdc12c4e9159c75e516cdc3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6470c6a4349ea591ce2bbcd93199f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee844c70ab064971860fb0a2b00acb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c567b816889a865372ed6fc8f2053392.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(ⅱ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927237ea7d037e88e678514213862ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81687c0af83f550bcb802e2d82c76a61.png)
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2 . 坐标法是解析几何中最基本的研究方法,坐标法是以坐标系为桥梁,把几何问题转化成代数问题,通过代数运算研究几何图形性质的方法.请利用坐标法解决以下问题:
(1)在直角坐标平面内,已知
,对任意
,试判断
的形状;
(2)在平面内,已知
中,
,
为
的中点,
交
于
,求证:
.
(1)在直角坐标平面内,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5e9ea0691daa797bd0889d7f5a6133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6057df53aac56374ddf8146623f64678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
(2)在平面内,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5034e2d0d1bd5792403a62df2c950e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a9bd800bdf8f09e56bb8c9de37de34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4517371dfbf00378551aaae1a04ecc99.png)
![](https://img.xkw.com/dksih/QBM/2012/2/11/1570731291418624/1570731297046528/STEM/9d2658a7-8285-49f8-b3ff-e0b9a325dcad.png?resizew=146)
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2018高三·全国·专题练习
3 . 已知椭圆
经过点
,其离心率为
,设直线
与椭圆
相交于
两点.
(1)求椭圆
的方程;
(2)已知直线
与圆
相切,求证:
(
为坐标原点);
(3)以线段
为邻边作平行四边形
,若点
在椭圆
上,且满足
(
为坐标原点),求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261ca562ba1c9f5595b08eae6f40ce20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c83f9e7f57d03304c3d0e51f43aa5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(3)以线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913bb2ec28f1de10d23785e060cde496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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