12-13高二上·广东湛江·期末
1 . 已知椭圆
经过点
,O为坐标原点,平行于OM的直线l在y轴上的截距为
.
(1)当
时,判断直线l与椭圆的位置关系(写出结论,不需证明);
(2)当
时,P为椭圆上的动点,求点P到直线l距离的最小值;
(3)如图,当l交椭圆于A、B两个不同点时,求证:直线MA、MB与x轴始终围成一个等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a667af488582538fc08d8e454d5543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bea681006f614f8a070e9c6a942c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41b8856f1acaf13e6968f0a96f37795.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f7bc699f2bf19dd5a7635375cd3c8e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f7bc699f2bf19dd5a7635375cd3c8e.png)
(3)如图,当l交椭圆于A、B两个不同点时,求证:直线MA、MB与x轴始终围成一个等腰三角形.
![](https://img.xkw.com/dksih/QBM/2012/1/16/1570692813488128/1570692819148800/STEM/c8ea6302-eb33-4b32-834e-0c3f11680e2c.png?resizew=221)
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2 . 在平面直角坐标系xOy中,已知椭圆
.如图所示,斜率为k(k>0)且不过原点的直线l交椭圆C于A,B两点,线段AB的中点为E,射线OE交椭圆C于点G,交直线x=﹣3于点D(﹣3,m).
(1)求m2+k2的最小值;
(2)若|OG|2=|OD|∙|OE|,
(i)求证:直线l过定点;
(ii)试问点B,G能否关于x轴对称?若能,求出此时△ABG的外接圆方程;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4d3fac09fb943b5da320395ff0879a.png)
(1)求m2+k2的最小值;
(2)若|OG|2=|OD|∙|OE|,
(i)求证:直线l过定点;
(ii)试问点B,G能否关于x轴对称?若能,求出此时△ABG的外接圆方程;若不能,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/489c2274-66e7-4655-aeeb-9a6b7820e184.png?resizew=218)
您最近一年使用:0次
2016-12-03更新
|
3325次组卷
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4卷引用:2011年普通高等学校招生全国统一考试文科数学(山东卷)
2011年普通高等学校招生全国统一考试文科数学(山东卷)天津市静海县第一中学2017-2018学年高二上学期期末终结性检测数学(理)试题(附加题)(已下线)专题45 盘点圆锥曲线中的定点问题——备战2022年高考数学二轮复习常考点专题突破(已下线)第五篇 向量与几何 专题5 调和点列 微点3 调和点列(三)
11-12高二上·广东·期中
3 . 一圆形纸片的半径为10cm,圆心为
,
为圆内一定点,
cm,
为圆周上任意一点,把圆纸片折叠,使
与
重合,然后抹平纸片,这样就得到一条折痕
,设
与
交于
点,如图
(1)求点
的轨迹方程;
(2)求证:直线
为点
轨迹的切线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee31576bd3f8ebe604e5b7a44f82990b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2011/12/13/1570573903536128/1570573909229568/STEM/69f4fbb601db4ca69ba6218f2c60e317.png?resizew=164)
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11-12高二上·福建泉州·期末
解题方法
4 . 如图,已知椭圆
的离心率为
,短轴的一个端点到右焦点的距离为
.设直线
与椭圆
相交于
两点,点
关于
轴对称点为
.
(1)求椭圆
的方程;
(2)若以线段
为直径的圆过坐标原点
,求直线
的方程;
(3)试问:当
变化时,直线
与
轴是否交于一个定点?若是,请写出定点的坐标,并证明你的结论;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9b0ea1fff6a9a3760b922b77ac0c64.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d7ffb7889a31b267a85f1ea238138e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若以线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)试问:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9806df6df27bf715c81c4a93fc6517c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2011/3/11/1570035519168512/1570035524771840/STEM/08d7aa31d65342409b75100b77a878b2.png?resizew=227)
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11-12高三上·北京东城·期末
解题方法
5 . 已知椭圆
的左、右焦点分别为
,过点
且不与坐标轴垂直的直线
与椭圆
交于
两点.
(1)求直线
的斜率的取值范围;
(2)若点
在椭圆
上,且
三点共线,求证:点
与点
的横坐标相同.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc8350b12974ffc8d06fce36d158f02.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/7789a500686c7a73770404ead6af0590.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7445eabdcf8054f3ba700faf3adf09c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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10-11高三上·江西吉安·开学考试
6 . 设
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5205b8313b70d74c193469bac5b6b86.png)
(1)求证:函数y=f(x)与y=g(x)的图像有两个交点;
(2)设f(x)与g(x)的图像交点A、B在x轴上的射影为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4753463638237ed69779fff0c66746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5205b8313b70d74c193469bac5b6b86.png)
(1)求证:函数y=f(x)与y=g(x)的图像有两个交点;
(2)设f(x)与g(x)的图像交点A、B在x轴上的射影为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7dbd8f93574f91414274b354adf934.png)
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9-10高二下·河北石家庄·期中
7 . 椭圆
+
=1(a>b>0)与直线x+y-1=0相交于P,Q两点,且
⊥
(O为坐标原点).
(1)求证:
+
等于定值;
(2)若椭圆的离心率e∈[
,
],求椭圆长轴长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf6c83cb6c14b1e4c5b62971cd0ec43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb79009bf32bee98374d74b54050351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6366a4f22d1b16b2f185e7eaba32256d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652514a62f1099e767a78c5f681c4717.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd2d9768fa893cbc19074ed2991301e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27a46adf90be46555024bb17117bf84.png)
(2)若椭圆的离心率e∈[
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4d9ff190d74979422dae71751c6fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.png)
您最近一年使用:0次
2016-11-30更新
|
901次组卷
|
3卷引用:2010年河北省正定中学高二下学期期中考试数学(文)
(已下线)2010年河北省正定中学高二下学期期中考试数学(文)辽宁省大连渤海高级中学2017-2018学年高二上学期期中考试数学(理)试题湖北省荆州成丰学校2017-2018学年高二3月月考文科数学试题