解题方法
1 . 在直角坐标系xOy中,已知点
,直线AM,BM交于点M,且直线AM与直线BM的斜率满足:
.
(1)求点M的轨迹C的方程;
(2)设直线l交曲线C于P,Q两点,若直线AP与直线AQ的斜率之积等于-2,证明:直线l过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9e61a7c470be817b2de725460ddd66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298fa44e15f92fc6b5fc90eee2b019b2.png)
(1)求点M的轨迹C的方程;
(2)设直线l交曲线C于P,Q两点,若直线AP与直线AQ的斜率之积等于-2,证明:直线l过定点.
您最近一年使用:0次
2023-05-31更新
|
415次组卷
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2卷引用:2.4.2直线与圆锥曲线的综合问题 2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册
2021·全国·模拟预测
名校
解题方法
2 . 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)
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2021-12-31更新
|
1143次组卷
|
4卷引用:2022年全国高中名校名师原创预测卷(九)
2021·全国·模拟预测
解题方法
3 . 已知椭圆C:
的离心率为
,
,
分别为椭圆C的左、右焦点,过
且与x轴垂直的直线与椭圆C交于点A,B,且
的面积为
.
(1)求椭圆C的标准方程;
(2)设直线l与椭圆C交于不同于右顶点P的M,N两点,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C的标准方程;
(2)设直线l与椭圆C交于不同于右顶点P的M,N两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3835e6398d18d162afebc92cd2ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
您最近一年使用:0次
2021·全国·模拟预测
4 . 已知抛物线
的焦点为F,过点F的直线l交抛物线C于A,B两点,当
轴时,
.
(1)求抛物线C的方程;
(2)若直线l交y轴于点D,过点D且垂直于y轴的直线交抛物线C于点P,直线PF交抛物线C于另一点Q.
①是否存在定点M,使得四边形AQBM为平行四边形?若存在,求出定点M的坐标;若不存在,请说明理由.
②求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165a501b2e6a3acc46212e59a166c053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
(1)求抛物线C的方程;
(2)若直线l交y轴于点D,过点D且垂直于y轴的直线交抛物线C于点P,直线PF交抛物线C于另一点Q.
①是否存在定点M,使得四边形AQBM为平行四边形?若存在,求出定点M的坐标;若不存在,请说明理由.
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8278d203835f418911b24159b104a70.png)
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名校
解题方法
5 . 已知椭圆
(
)与椭圆
的焦点相同,且椭圆C过点
.
(1)求椭圆C的方程;
(2)是否存在圆心在原点的圆,使得该圆的任意一条切线与椭圆C恒有两个交点A,B,且
,(O为坐标原点),若存在,求出该圆的方程;若不存在,说明理由;
(3)P是椭圆C上异于上顶点
,下顶点
的任一点,直线
,
,分别交x轴于点N,M,若直线OT与过点M,N的圆G相切,切点为T.证明:线段OT的长为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2603ea55ff8561111b46b1dd99172347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f4aad2e5282f87f561e6aa91d0a32a.png)
(1)求椭圆C的方程;
(2)是否存在圆心在原点的圆,使得该圆的任意一条切线与椭圆C恒有两个交点A,B,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(3)P是椭圆C上异于上顶点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
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2021-12-06更新
|
1185次组卷
|
3卷引用:四川省成都市树德中学2021-2022学年高二上学期11月阶段性测试数学(理科)试题
四川省成都市树德中学2021-2022学年高二上学期11月阶段性测试数学(理科)试题四川省成都市第七中学2021-2022学年高二上学期12月阶段性测试数学(理)试题(已下线)专题3.16 圆锥曲线中的定点、定值问题大题专项训练(30道)-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)
解题方法
6 . 1.已知点
,
,动点
满足直线
的斜率与直线
的斜率乘积为
.当
时,点
的轨迹为
;当
时,点
的轨迹为
.
(1)求
,
的方程.
(2)是否存在过
右焦点的直线
,满足直线
与
交于
,
两点,直线
与
交于
,
两点,且
?若存在,求所有满足条件的直线
的斜率之积;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0a96569d3ae91b7c61cbb8ba22a018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1c567b22c69c1c96a5bb71181b7170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
(2)是否存在过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.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/0cd5dac19a3fa0ffa7f160275691ca70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
7 . 1.已知椭圆
),离心率为
,如图,
是圆M:
的一条直径,若椭圆E经过A、B两点.
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844302535319552/2844859362041856/STEM/8c2f069143c146d2bce64f80cde26f30.png?resizew=250)
(1)求椭圆E的方程.
(2)点P为椭圆E上一个动点,求△
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e771212eddd31a7c33c284f65caf656.png)
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844302535319552/2844859362041856/STEM/8c2f069143c146d2bce64f80cde26f30.png?resizew=250)
(1)求椭圆E的方程.
(2)点P为椭圆E上一个动点,求△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2021高三·全国·专题练习
解题方法
8 . 已知椭圆
的左顶点为A,过A作两条弦AM、AN分别交椭圆于M、N两点,直线AM、AN的斜率记为
,满足
,则直线MN经过的定点为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985a294d39f2a106aa474462ec15dbfb.png)
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解题方法
9 . 已知抛物线
,过
的直线交抛物线C于A、B两点.若点P是抛物线上A、B之间一点,当点P到直线
的距离最大时,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
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10 . 椭圆
的右顶点为A,上顶点为B,O为坐标原点,直线
的斜率为
,
的面积为1.
(1)求椭圆的标准方程;
(2)椭圆上有两点M,N(异于椭圆顶点,且MN与x轴不垂直),证明:当
的面积最大时,直线
与
的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(1)求椭圆的标准方程;
(2)椭圆上有两点M,N(异于椭圆顶点,且MN与x轴不垂直),证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
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2021-09-04更新
|
3364次组卷
|
9卷引用:湖南省娄底市双峰县第一中学2021-2022学年高三上学期入学摸底考试数学试题
湖南省娄底市双峰县第一中学2021-2022学年高三上学期入学摸底考试数学试题(已下线)专题04 圆锥曲线定值问题-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)山东省德州市2021-2022学年高三上学期12月月考数学试题重庆市万州纯阳中学2021-2022学年高二上学期12月月考(B卷)数学试题湖南省天壹名校联盟2021-2022学年高三上学期入学摸底考试数学试题(已下线)第十一章 圆锥曲线专练14—椭圆大题(证明题)-2022届高三数学一轮复习重庆市朝阳中学2021-2022学年高二上学期12月月考数学试题(已下线)专题22 圆锥曲线中的定点、定值、定直线问题 微点2 圆锥曲线中的定值问题新疆维吾尔自治区乌鲁木齐市第101中学2022-2023学年高二上学期12月月考数学试题