解题方法
1 . 过抛物线
焦点F的直线与抛物线交于A,B两点,
,抛物线的准线与x轴交于点C,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dafa31b2ce744f96c483b9dc55a16ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37eac93736b605958ab6834b255dfa8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
2 . 已知椭圆C:
的一个焦点与抛物线
的焦点F重合,抛物线的准线被C截得的线段长为
.
(1)求椭圆C的方程;
(2)过点F作直线l交C于A,B两点,试问:在x轴上是否存在一个定点M,使
为定值?若存在,求出M的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求椭圆C的方程;
(2)过点F作直线l交C于A,B两点,试问:在x轴上是否存在一个定点M,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787dfab61ed9830b531da365e592bbd.png)
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解题方法
3 . 已知椭圆
经过点
,下顶点
为抛物线
的焦点.
(1)求椭圆
的方程;
(2)若点
均在椭圆
上,且满足直线
与
的斜率之积为
,
(ⅰ)求证:直线
过定点;
(ⅱ)当
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cfeb2ed775551c13dba49b40005253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d213f131f206f5f3520860de56690.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2052732179abb51957769c28939b4358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(ⅰ)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4a8940130ef85d5c57abf7b1c0fe19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2024-03-24更新
|
499次组卷
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4卷引用:2024届天津市耀华中学高三二模数学试卷
名校
解题方法
4 . 设椭圆
的一个顶点与抛物线
的焦点重合,
分别是椭圆的左、右焦点,离心率
,过椭圆右焦点
的直线
与椭圆
交于
两点.
(1)求椭圆
的方程;
(2)若
,求直线
的方程;
(3)已知直线
斜率存在,若
是椭圆
经过原点
的弦,且
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce21531a886c50568b75fd4278f15dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd38f55d7cdae1de6e2a2e2c6e1e57d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964889aaf14b9ef1837a988c048788e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24caeb80a748bcbc9dc33cd430a5aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1a3c79973f7fa2547db303c1279277.png)
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解题方法
5 . 已知抛物线
的焦点为F,直线l过焦点F与C交于A,B两点,以
为直径的圆与y轴交于D,E两点,且
,则直线l的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6df3d34b75369313c9d2c7eb1b26f29.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-10-28更新
|
4236次组卷
|
17卷引用:天津市崇化中学2022-2023学年高二上学期期末数学试题
天津市崇化中学2022-2023学年高二上学期期末数学试题天津市南开大学附中2023-2024学年高二上学期第二次月考数学试题湖北省十堰市丹江口市第一中学2021-2022学年高三下学期模拟数学试题(二)(已下线)第03讲 抛物线(练)四川省绵阳南山中学2022-2023学年高二上学期期中考试理科数学试题重庆市南开中学校2022-2023学年高二上学期网课质量检测数学试题(已下线)模拟卷04(已下线)专题9-4 抛物线性质应用归类-2(已下线)专题9-4 抛物线性质应用归类-3湖北省武汉市第六中学2022-2023学年高二上学期第三次月考数学试题陕西省西安工业大学附属中学2022-2023学年高三上学期第六次适应性考试理科数学试题浙江省杭州市2022-2023学年高三上学期第一次质量检测(期末)数学试题(已下线)新高考卷04云南省曲靖市宣威市第七中学2023届高三高考数学学情检测数学试题(一)浙江省杭州市2023届高三上学期教学质量检测数学试题江西省宜春市宜丰县宜丰中学2022-2023学年高二上学期第三次月考(12月)数学试题浙江省宁波市鄞州中学2023-2024学年高二上学期期中考试数学试题
6 . 已知椭圆
的中心在原点,离心率等于
,它的一个短轴端点恰好是抛物线
的焦点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/7bf103f9-bb71-4fb6-96ac-00163edcdfa1.png?resizew=194)
(1)求椭圆
的方程;
(2)已知
、
是椭圆上的两点,
,
是椭圆上位于直线
两侧的动点.
①若直线
的斜率为
,求四边形
面积的最大值;
②当
,
运动时,满足直线
、
与
轴始终围成一个以底边在
轴的等腰三角形,试问直线
的斜率是否为定值,请说明理由.
![](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/1f08dbfa20abb0850491515174ce1cb0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/7bf103f9-bb71-4fb6-96ac-00163edcdfa1.png?resizew=194)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f6a03826a5ad351c1f7ca553a6945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561fbd802d8f840ebb1086a97aca3f70.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/7a5f1641947153c80b987320885a2b57.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
②当
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
7 . 设椭圆
的一个顶点与抛物线
的焦点重合,
、
分别是椭圆
的左、右焦点,离心率
,过椭圆
右焦点
的直线
与椭圆
交于
、
两点.
(1)求椭圆
的方程;
(2)是否存在直线
,使得
,若存在,求出直线
的方程;若不存在,说明理由;
(3)设点
是一个动点,若直线
的斜率存在,且
为
中点,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcede16b21958999784badebec351264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c42aaa43a1a479b04760c6f58eaf5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d658841bbf114c975e355a1d04bf77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
(2)是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b4e99f09f90484a9786629f5fef6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fb2a6dcbbbc1e01f4b835438edfdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9eeee83b4b7c6ceac7828ff534ce15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282f15590a18638fa0f3ec8475b1929f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08075b3b73dd2609baad69a496fdd9a8.png)
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8 . 抛物线
的准线l与双曲线C:
(
,
)交于A、B两点,
,
为曲线C的左右焦点,
在l左边,
为等边三角形,
与双曲线的一条渐近线交于E点,
,则
的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48f220f8fc1cb2c4e8ceffec9e2015a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ff8a5886e42095da57422c8777c10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3de873f9e63408a3b60bacea31f27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1bfa28468ac6174f344af895a3534e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-04-29更新
|
1177次组卷
|
6卷引用:天津市第四十七中学2021-2022学年高三上学期第二次月考数学试题
9 . 已知椭圆C的中心在原点,离心率等于
,它的一个短轴端点恰好是抛物线
的焦点.
(1)求椭圆C的方程;
(2)如图,已知
,
是椭圆上的两点,A,B是椭圆上位于直线PQ两侧的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/9690d344-64d2-42b7-bd11-842e6185bfd7.png?resizew=208)
①若直线AB的斜率为
,求四边形APBQ面积的最大值;
②当A,B运动时,满足
,试问直线AB的斜率是否为定值?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85027cef6f6920c2a38edec6ba5e7fcf.png)
(1)求椭圆C的方程;
(2)如图,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea812262436710ea0f205341861719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7945f6295f1d9cb6cdd4029c6253fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/9690d344-64d2-42b7-bd11-842e6185bfd7.png?resizew=208)
①若直线AB的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②当A,B运动时,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198c249705ffdee268cd836f382e3855.png)
您最近一年使用:0次
2021-01-17更新
|
309次组卷
|
4卷引用:2017届天津市红桥区重点中学八校高三4月联考数学(文)试卷
2017届天津市红桥区重点中学八校高三4月联考数学(文)试卷湖南省衡阳市田家炳实验中学2020-2021学年高三上学期12月月考数学试题江苏省南京市第十二中学2020-2021学年高二上学期第一次学情调研测试数学试题(已下线)模型1 圆锥曲线中的几何图形模型(高中数学模型大归纳)
名校
解题方法
10 . 已知
,
分别是椭圆
:
的左,右焦点,点
在椭圆
上,且抛物线
的焦点是椭圆
的一个焦点.
(1)求
,
的值:
(2)过点
作不与
轴重合的直线
,设
与圆
相交于A,B两点,且与椭圆
相交于C,D两点,当
时,求△
的面积.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c48fe1b9d24ccd12aec18e338cabcef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567f6afff62e89a6eedd383735458f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求
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14卷引用:天津市第七中学2021-2022学年高三上学期第一次月考数学试题
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