13-14高二上·安徽池州·期中
1 . 矩形
的中心在坐标原点,边
与
轴平行,
=8,
=6.
分别是矩形四条边的中点,
是线段
的四等分点,
是线段
的四等分点.设直线
与
,
与
,
与
的交点依次为
.
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/57f1591ebeb842f19cbd763b71f91200.png)
(1)以
为长轴,以
为短轴的椭圆Q的方程;
(2)根据条件可判定点
都在(1)中的椭圆Q上,请以点L为例,给出证明(即证明点L在椭圆Q上).
(3)设线段
的
(
等分点从左向右依次为
,线段
的
等分点从上向下依次为
,那么直线
与哪条直线的交点一定在椭圆Q上?(写出结果即可,此问不要求证明)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/435b32cf5c70495d8a9d4ae686403b4e.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/f9e9f76a62c94107aede2953c25c254a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/6759f0b6901340f8b45b2dd7c9b0f686.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/f9e9f76a62c94107aede2953c25c254a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/0944b5e4d0eb448480b8a5ed7701764f.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/8b4d9f94de0845cca892771d54aaa380.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/4af4218c3ee24fa2a45bc052a533e366.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/86c3196595864ed987d9176ce60110d3.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/1c89e7ef630a4caebd00a40541db89e2.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/52b21f978fec4d919d0ce9514f5c5c6a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/7cf316df36354570b9695d8b198bc600.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/1ec51823a90b49449b4cb9df6d8e6d8a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/4dd956b823c240a6aee2a935734e2b45.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/f24db0921c334e5f9d168df0f09a7da8.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/a40af3c63639460a8bd0aa73dc5c35a6.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/e163e696296f496c807f6906f549a775.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/ff27d02022384d009917f6cdb1641ce6.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/57f1591ebeb842f19cbd763b71f91200.png)
(1)以
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/22b901d8dabe44fd9eab93ed4dc7aa4d.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/ec4d271858b64924b9da55af5ca50212.png)
(2)根据条件可判定点
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/ff27d02022384d009917f6cdb1641ce6.png)
(3)设线段
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/86c3196595864ed987d9176ce60110d3.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/a850fcc7040e43a3b14bd41677fb5a13.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/9583e5aee617486aa2d5793549fbd241.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/5e49a32f835f41aa875bc23536562cf0.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/52b21f978fec4d919d0ce9514f5c5c6a.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/a850fcc7040e43a3b14bd41677fb5a13.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/a961e17883464621a631d89b586232bf.png)
![](https://img.xkw.com/dksih/QBM/2014/1/3/1571457090797568/1571457096687616/STEM/b5b5ffc22ad344929af9d7d5b7f748d4.png)
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解题方法
2 . 已知椭圆C:
,左、右顶点分别为
.
(1)设直线l:
与x轴交于点D,P点是椭圆C异于
的动点,直线
,
分别交直线l于E,F两点,求证:
为定值.
(2)如图,原点O到
:
距离为1,直线
与椭圆C交于A,B两点,直线
:
与
平行且与椭圆C相切于点M(O,M位于直线
的两侧).记
,
的面积分别为
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82766cfd2b7c59c7fac5b827ae5863b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/96ec2d8d-9e09-4df9-acc0-c73cc8d1512b.png?resizew=180)
(1)设直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64dd02a89474b1d9e982b0f36bdfc4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4467ae87f85c64f86baa1205a3f79b5.png)
(2)如图,原点O到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054806a29234e3eb2d07f07a85f0dbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5777fb059759ad10ccb602be54a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
3 . 已知椭圆
的焦点
,且椭圆
的离心率为
.
(1)求椭圆
的方程;
(2)若
、
为
上不同的两点,动点
、
满足:
,
,且
在
上.
(i)求证:点
在
上;
(ii)若
过焦点
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/352c283e5e0316b9e27768db28296491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecef922a02b99afe79e373de2beb7646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(i)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2022-03-22更新
|
548次组卷
|
4卷引用:浙江省杭州学军中学西溪校区2021-2022学年高二下学期4月期中数学试题
4 . 已知
的长轴长为4,短轴长为2.
(1)求椭圆C的标准方程;
(2)点A,B分别为椭圆C的左、右顶点,点P为椭圆C上的动点(异于A,B两点),过原点O作直线PB的垂线,垂足为H,直线OH与直线AP相交于点M,证明:点M的横坐标为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
(1)求椭圆C的标准方程;
(2)点A,B分别为椭圆C的左、右顶点,点P为椭圆C上的动点(异于A,B两点),过原点O作直线PB的垂线,垂足为H,直线OH与直线AP相交于点M,证明:点M的横坐标为定值.
您最近一年使用:0次
2021-01-27更新
|
865次组卷
|
5卷引用:青海省海东市第一中学2023-2024学年高二上学期期中考试数学试题
解题方法
5 . 已知焦距为2的椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a4cd7199b171703f8064bc7e7a730f.png)
(
)的左、右顶点分别为
,上、下顶点分别为
,点
为椭圆
上不在坐标轴上的任意一点,且四条直线
的斜率之积为
.
(1)求椭圆
的标准方程;
(2)如图所示,点
是椭圆
上两点,点A与点B关于原点对称,
,点 C 在 x 轴上,且
与 x 轴垂直,求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a4cd7199b171703f8064bc7e7a730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2988e435ffb7935d49569ee824262f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d283e0523608b39609658a238946d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9dde7e3a164b37c806872ef8430a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)如图所示,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663aa29cf0f19e37809eb6ea70c4e767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d1fdf1d417bf19e377e44d279014d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/10e66bbc-e8cb-443b-ad7d-5e71b5f21e5e.png?resizew=151)
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