直角坐标系
中,已知椭圆
的左,右焦点分别为
,
,
为
的中点,过
作直线交椭圆于
,
两点,过
作另一直线交椭圆于
,
两点.
(1)判断以
为直径的圆是否经过
,若经过,请求出此时
的斜率,若不经过请说明理由;
(2)若
,
,
三点共线,设直线
与直线
的斜率存在且分别为
,
,试问
是否为常数,若是,求出常数的值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f507af94d93bab9e1bda4a214e8f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d107e77106ff1a9cb76b504bbc99bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)判断以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a3f348a942d468f0d77c0dfbb41d87.png)
2020·全国·模拟预测 查看更多[4]
2020年普通高等学校招生全国统一考试(全国2卷)理科数学试题(白卷)(已下线)黄金卷05-【赢在高考·黄金20卷】备战2021年高考数学(理)全真模拟卷(新课标Ⅲ卷)(已下线)黄金卷03-【赢在高考·黄金20卷】备战2021年高考数学(理)全真模拟卷(新课标Ⅱ卷)(已下线)黄金卷02-【赢在高考·黄金20卷】备战2021年高考数学(文)全真模拟卷(新课标Ⅱ卷)
更新时间:2020-07-29 15:55:33
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相似题推荐
解答题-证明题
|
困难
(0.15)
解题方法
【推荐1】如图,点A、B、C分别为椭圆
的左、右顶点和上顶点,点P是
上在第一象限内的动点,直线AP与直线BC相交于点Q,直线CP与x轴相交于点M.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/7af96dc5-c1f6-43a1-8434-369b5878f73e.png?resizew=283)
(1)求直线BC的方程;
(2)求证:
;
(3)已知直线
的方程为
,线段QM的中点为T,是否存在垂直于y轴的直线
,使得点T到
和
的距离之积为定值?若存在,求出
的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b1b8a84ae7a1b2243b78cc932860d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/7af96dc5-c1f6-43a1-8434-369b5878f73e.png?resizew=283)
(1)求直线BC的方程;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba1480cc9c2f1a5128336a7818f8189.png)
(3)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aa3adcb154f6144903d456289ecb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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【推荐2】函数
是我们最熟悉的函数之一,它是奇函数,且y轴和直线
是它的渐近线,在第一象限和第三象限存在图象,其图象实质是圆锥曲线中的双曲线.
的图象不仅是中心对称图形,而且还是轴对称图形,求其对称轴l的方程;
(2)若保持原点不动,长度单位不变,只改变坐标轴的方向的坐标系的变换,叫坐标系的旋转,简称转轴.
(i)请采用适当的变换方法,求函数
变换后所对应的双曲线标准方程;
(ii)已知函数
图象上任一点到平面内定点
的距离差的绝对值为定值,以线段
为直径的圆与
的图象一个交点为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
(2)若保持原点不动,长度单位不变,只改变坐标轴的方向的坐标系的变换,叫坐标系的旋转,简称转轴.
(i)请采用适当的变换方法,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
(ii)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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【推荐3】如图1,直线
与x轴,y轴分别相交于A,B两点,将
绕点O逆时针旋转90°得到
,过点A,B,D的抛物线
叫做l的关联抛物线,而直线l叫做
的关联直线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ef9d3ce4-d4b1-4552-a814-082583273cf8.png?resizew=458)
(1)若直线
,则抛物线
表示的函数解析式为________;若抛物线
,则直线l表示的函数解析式为______.
(2)求抛物线
的对称轴(用含m,n的代数式表示);
(3)如图2,若直线
,抛物线
的对称轴与
相交于点E,点F在l上,点Q在抛物线
的对称轴上.当以点C,E,Q,F为顶点的四边形是以
为一边的平行四边形时,求点Q的坐标;
(4)如图3,若直线
,G为
中点,H为
中点,连接
,M为
中点,连接
.若
,求直线l,抛物线
表示的函数解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a88699a9cab3fb5e061e722d1f60a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9a6eeeebf3cff569578d7366b755aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ef9d3ce4-d4b1-4552-a814-082583273cf8.png?resizew=458)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90717234dbf965e8cb5f8fe2e53776da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef60818f89bebb4ed87db774a5149fd9.png)
(2)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
(3)如图2,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ec899da04f19dca04bba10ffc4358a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(4)如图3,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a163a3df8d98950645d7a249141b679d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc91a53e2534ce7034372b0add103eac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
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【推荐1】已知椭圆
经过点
,离心率为
,左右焦点分别为
,
.
(1)求椭圆
的方程;
(2)
是
上异于
的两点,若直线
与直线
的斜率之积为
,证明:
两点的横坐标之和为常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f034ca3728461235578233174da40e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cfa1e7ffae662aefb49a44c52d4954d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace7c9e3da8613175ca07c54c116127a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affbbbc112ab58e6b7066ce1c7699db0.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/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
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【推荐2】已知
分别为椭圆C:
的左、右焦点,点
在椭圆上,且
轴,
的周长为6.
(Ⅰ)求椭圆的标准方程;
(Ⅱ)E,F是椭圆C上异于点
的两个动点,如果直线PE与直线PF的倾斜角互补,证明:直线EF的斜率为定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882651b776851f3f0665de12da6ed47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0e2297e289632ffc211bd20e2e772e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1434a7398f22cb12bd74b8837628232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a846139a5dee6762bb7193273da66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7155284dd936a234de37b151850503d7.png)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)E,F是椭圆C上异于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐1】已知椭圆
的短轴长为2,且经过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e76c61a9779156672989ed0e5ff6b9a.png)
(1)求椭圆C的标准方程;
(2)设直线l与椭圆C交于A,B两点,已知
,若
为定值,则直线l是否经过定点?若经过,求出定点坐标和定值;若不经过,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e76c61a9779156672989ed0e5ff6b9a.png)
(1)求椭圆C的标准方程;
(2)设直线l与椭圆C交于A,B两点,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de66a86daba661b3bc05c6a073ac4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787dfab61ed9830b531da365e592bbd.png)
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【推荐2】已知椭圆
:
过点
,且离心率为
,过点
的直线
与椭圆
交于
,
两点.
(1)求椭圆
的标准方程;
(2)若点
为椭圆
的右顶点,探究:
是否为定值,若是,求出该定值,若不是,请说明理由.(其中,
,
分别是直线
、
的斜率)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfdd0414492894e63277223fddfe2ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668d61a88b296ebd55a3b0bbc277539a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f63e9a213f3dd57269cf4ff02d6212e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1456e81321ccb20077b34562ca9cffbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090b7ee52d644d0c630ef44aec1726dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
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【推荐1】已知椭圆
,
,
分别为椭圆
的右顶点、上顶点,
为椭圆
的右焦点,椭圆
的离心率为
,
的面积为
.
(1)求椭圆
的标准方程;
(2)过点
作直线交椭圆于
,
两点,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23686d37eb89fb4c6b6649fb76f02b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/89d8dea222790d161280aaf3cba7dd30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解答题-证明题
|
困难
(0.15)
解题方法
【推荐2】已知椭圆
:
(
)的左,右焦点为
,
,离心率为
,点
是椭圆
上不同于顶点的任意一点,射线
,
分别与椭圆
交于点
,
,
的周长为8.
(1)求椭圆
的标准方程;
(2)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](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/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/8144da365530cc0560de2d4946c96a1d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5a29b7ed0c415987dfc800850231a2.png)
您最近一年使用:0次