9-10高二下·黑龙江·期末
1 . 已知椭圆
过点
,且离心率
.
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/942052b9cbdd4a9fa8ad2b0d7d1f3110.png)
(Ⅰ)求椭圆方程;
(Ⅱ)若直线
与椭圆交于不同的两点
、
,且线段
的垂直平分线过定点
,求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/8ce15a373433487bb6753ddd3209fed4.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/69ae5024587b4d23a30f110bee47fbe2.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/5efcbacb9aea437d95f68e2a7117bd8a.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/942052b9cbdd4a9fa8ad2b0d7d1f3110.png)
(Ⅰ)求椭圆方程;
(Ⅱ)若直线
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/67f5912d46374f3b883a4f1487fb4de6.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/8e64dc7f52ea4d6ab889ebd444a29297.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/b1ec3990bc6744e79b2ade5b8bf8a6b7.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/b075ea9e030d43c98708e9b306ab9510.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/a5f078b9c15f421e97e67987b69e7955.png)
![](https://img.xkw.com/dksih/QBM/2012/12/28/1571084567977984/1571084573515776/STEM/bf13fc47f5a5481886340b68f2a970dd.png)
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12-13高三上·黑龙江牡丹江·期末
2 . 已知椭圆
经过点
,离心率为
,直线
经过椭圆
的右焦点
交椭圆于
两点,点
在直线
上的射影依次为点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/0452e419-64d9-4308-af77-28e2497baeb2.png?resizew=199)
(1)求椭圆
的方程;
(2)若直线
交
轴于点
,且
,当直线
的倾斜角变化时,探求
的值是否为定值?若是,求出
的值,否则,说明理由;
(3)连接
,试探索当直线
的倾斜角变化时,直线
与
是否相交于定点?若是,请求出定点的坐标,并给予证明;否则,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4c2e693b99f17d7165d421c9ca9067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca263cd4e8575dbe12b6d5b26ceb5d98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/0452e419-64d9-4308-af77-28e2497baeb2.png?resizew=199)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2149211608e0d883495fd1fee555198b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e88ee337b7c9082f4fe84fd1752d55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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12-13高二上·黑龙江·期末
名校
3 . 如图,边长为
的等边
所在的平面垂直于矩形
所在的平面,
,
为
的中点.
(1)证明:
;
(2)求异面直线
和
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbcc91180cb7cc891f78dd3b1516e697.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2012/2/9/1570725115961344/1570725121056768/STEM/c8774bd6-6732-44f3-a3a5-b73455b7aaf3.png?resizew=260)
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12-13高三上·黑龙江哈尔滨·期末
4 . 如图,已知椭圆C:
,经过椭圆C的右焦点F且斜率为k(k≠0)的直线
交椭圆C于A、B两点,M为线段AB的中点,设O为椭圆的中心,射线OM交椭圆于N点.是否存在k,使对任意m>0,总有
成立?若存在,求出所有k的值;
![](https://img.xkw.com/dksih/QBM/2012/2/6/1570718630895616/1570718636384256/STEM/f5f975d3046345f3a748ca9a42f7b747.png)
![](https://img.xkw.com/dksih/QBM/2012/2/6/1570718630895616/1570718636384256/STEM/604598683c0e4951ad1e4c4c8658b033.png)
![](https://img.xkw.com/dksih/QBM/2012/2/6/1570718630895616/1570718636384256/STEM/38269f83d5b14f74ad521e4cdc33ee77.png)
![](https://img.xkw.com/dksih/QBM/2012/2/6/1570718630895616/1570718636384256/STEM/cdd7b9c7c84f48eb9e0a2b6efe6a5d8b.png)
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12-13高三上·黑龙江大庆·期末
解题方法
5 . 已知椭圆
的长轴长为
,且点
在椭圆上.
(1)求椭圆的方程;
(2)过椭圆右焦点的直线
交椭圆于
两点,若以
为直径的圆过原点,求直线
方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dce10bf671cc2ebc67aa7fd568a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆的方程;
(2)过椭圆右焦点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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12-13高二上·黑龙江·期末
6 . 已知顶点在原点,焦点在x轴上的抛物线被直线y=2x+1截得的弦长为
.
(1)求抛物线的方程;
(2)若抛物线与直线y=2x﹣5无公共点,试在抛物线上求一点,使这点到直线y=2x﹣5的距离最短.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24291703cdec1e3d85e96779ed3c3647.png)
(1)求抛物线的方程;
(2)若抛物线与直线y=2x﹣5无公共点,试在抛物线上求一点,使这点到直线y=2x﹣5的距离最短.
您最近一年使用:0次
12-13高二上·黑龙江·期末
解题方法
7 . 求中心在坐标原点,对称轴为坐标轴且经过点
,一条渐近线的倾斜角为
的双曲线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685e73f420b856ebf5eb4eda574a4fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
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12-13高二上·黑龙江·期末
8 . 已知四棱锥P﹣ABCD的底面为直角梯形,AB∥DC,∠DAB=90°,PA⊥底面ABCD,且PA=AD=DC=1,AB=2,M是PB的中点.
(Ⅰ)证明:面PAD⊥面PCD;
(Ⅱ)求直线AC与PB所成角的余弦值;
(III)求面
与面
所成二面角的余弦值.
(Ⅰ)证明:面PAD⊥面PCD;
(Ⅱ)求直线AC与PB所成角的余弦值;
(III)求面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570684119769088/1570684125216768/STEM/a9f31976be134b0b9de0c78c3151ec92.png?resizew=233)
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11-12高三上·黑龙江大庆·期末
9 . 已知以向量
为方向向量的直线l过点
,抛物线
的顶点关于直线l的对称点在该抛物的准线上.
(Ⅰ)求抛物线C的方程;
(Ⅱ)设A、B是抛物线C上两个动点,过A作平行于x轴的直线m交直线OB于点N,若
(O为原点,A、B异于原点),试求点N的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a960240bf473c083a48e3f665d31a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba6562f59bb717a348d619e7b0c1654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
(Ⅰ)求抛物线C的方程;
(Ⅱ)设A、B是抛物线C上两个动点,过A作平行于x轴的直线m交直线OB于点N,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6672b7aa93c06da5ed1939824a03517a.png)
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