解题方法
1 . 已知抛物线
,
为E上一点,P到E的焦点F的距离为5.
(1)求E的标准方程;
(2)设O为坐标原点,A,B为抛物线E上异于P的两点,且满足
.
(ⅰ)判断直线
是否过定点,若过定点,求出定点的坐标;若不过定点,请说明理由;
(ⅱ)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4e5ecfd084f909f441631462d75e13.png)
(1)求E的标准方程;
(2)设O为坐标原点,A,B为抛物线E上异于P的两点,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
(ⅰ)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7dbc5f85292795579155dfd3baff0e.png)
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2 . 已知抛物线
的方程为
.
(1)若M是
上的一点,点N在
的准线l上,
的焦点为F,且
,
,求
;
(2)设
为圆
外一点,过P作
的两条切线,分别与
相交于点A,B和C,D,证明:当P在定直线
上运动时,
四点的纵坐标乘积为定值的充要条件为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
(1)若M是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb333b87ab3ecde430010b4dd8b371fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097f96fa2acd52a77bd9e2d3c33f53fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c5c639651fd0df8f041185e5c080b4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302981b9a0645b6439fb0febfb4b1caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee2abc983789634e0e57db4576e45b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc8335f8a3b076ccd596452bad61541.png)
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2023-09-08更新
|
718次组卷
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2卷引用:四川省部分学校2023-2024学年高三上学期9月联考理科数学试题
3 . 已知斜率为
的直线l与抛物线
相交于P,Q两点.
(1)求线段PQ中点纵坐标的值;
(2)已知点
,直线TP,TQ分别与抛物线相交于M,N两点(异于P,Q).则在y轴上是否存在一定点S,使得直线MN恒过该点?若存在,求出点S的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
(1)求线段PQ中点纵坐标的值;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b45d68e7ef26c34a15988283610c95c.png)
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名校
解题方法
4 . 已知斜率为
的直线
与抛物线
相交于
两点.
(1)求线段
中点纵坐标的值;
(2)已知点
,直线
分别与抛物线相交于
两点(异于
).求证:直线
恒过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c6eb7b48a27ad17219d724328b37cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce39b1e7a1021a1e574cd0611a09b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2023-05-09更新
|
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4卷引用:四川省成都市2023届高三三诊理科数学试题
四川省成都市2023届高三三诊理科数学试题四川省南充市阆中中学校2024届高三一模数学(理)试题四川省成都市石室天府中学2024届高三一诊模拟考试二数学(理)试题(已下线)第24讲 抛物线的简单几何性质6种常见考法归类(2)
5 . 已知点A在y轴右侧,点B,点C的坐标分别为
,
,直线AB,AC的斜率之积是3.
(1)求点A的轨迹D的方程;
(2)若抛物线
与点A的轨迹D交于E,F两点,过B作
于H,是否存在定点G使
为常数?若存在,求出G的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
(1)求点A的轨迹D的方程;
(2)若抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd27b64b553f69d1f8f550b9d5b093c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e966506a1e4f3e9a865169115b4da5fd.png)
您最近一年使用:0次
名校
解题方法
6 . 已知点
在
轴右侧,点
、点
的坐标分别为
、
,直线
、
的斜率之积是
.
(1)求点
的轨迹
的方程;
(2)若抛物线
与点
的轨迹
交于
、
两点,判断直线
是否过定点?若过定点,求出定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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2023-05-02更新
|
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3卷引用:四川省宜宾市2023届高三三模数学(文科)试题
名校
解题方法
7 . 过抛物线上的点
作直线交拋物线于另一点
.
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a2d2b2b666b03344637a73e05f5226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45193c02903d8966f135678c94fd840a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a17f9549fb066fcf191b42ae414c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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2023-03-23更新
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842次组卷
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6卷引用:四川省盐亭中学2023届高三第六次高考模拟检测数学理科试题
8 . 已知
为坐标原点,
是抛物线
上的动点,且
,过点
作
,垂足为
,下列各点中到点
的距离为定值的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efeccd375f7ee16b46cc1f5c22d1995f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:四川省叙永第一中学校2023-2024学年高三上学期零诊考试数学(理科)试题
四川省叙永第一中学校2023-2024学年高三上学期零诊考试数学(理科)试题山东省潍坊市2022-2023学年高三上学期期末数学试题安徽省合肥市庐阳高级中学2023届高三下学期5月模拟考试数学试题(已下线)重难专攻(九)?圆锥曲线中的定值问题(B素养提升卷)
名校
9 . 已知
为抛物线:
的焦点,过直线
上任一点
向抛物线引切线,切点分别为A,
,若点
在直线
上的射影为
,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a39b3b4d644c572cd92301f88e8cc4.png)
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3卷引用:四川省绵阳市2023届高三上学期第二次诊断性测试理科数学试题
名校
解题方法
10 . 已知抛物线
的焦点到准线的距离为1.
(1)求抛物线
的标准方程;
(2)设点
是该抛物线上一定点,过点
作圆
(其中
)的两条切线分别交抛物线
于点
,连接
.探究:直线
是否过一定点,若过,求出该定点坐标;若不经过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970e700ac6d59bf3eb78888385203b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f64da28829e4611733384ef78450a64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7910d0e12b74383a4914078b562038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2022-12-27更新
|
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4卷引用:四川省绵阳南山中学2023届高三下学期入学考试数学(理)试题
四川省绵阳南山中学2023届高三下学期入学考试数学(理)试题广西南宁市2023届高三上学期12月联考数学(文)试题(已下线)重难点突破13 切线与切点弦问题 (五大题型)(已下线)专题14抛物线专项练习