1 . 已知点S是圆
上任意一点,过S作x轴的垂线,垂足为H,点T满足
,记点T的轨迹为C.
(1)求轨迹C的方程;
(2)设轨迹C与x轴的交点分别为
,
,与y轴正半轴的交点为B,M是轨迹C上任意一点,且M不在坐标轴上.若直线
与直线
交于点P,直线
与直线
交于点Q.试判断
的形状,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13c02c5acb8df76da6356e504ded016.png)
(1)求轨迹C的方程;
(2)设轨迹C与x轴的交点分别为
![](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/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668438e15423368cd744445e824d18a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
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解题方法
2 . 如图,已知抛物线
,
为其准线.
为
上一动点,过点
作
于
,直线
交抛物线于点
.若直线
过定点
.
(1)求
的值;
(2)过抛物线
上一动点
作抛物线
的两条切线,切点为
、
.记
的外心为
.证明:以
为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a9efe4c27ce894634c9e4c737b5fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb50782b4a4f59f8798a90086b0d5c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74973a2eb4281a6943a506b779740ca7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/2/c8b920e2-0711-4e77-866a-534d8d8da985.png?resizew=126)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b57041b43206fc0d477f8c769078f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d48de5a380ae57e1094720433ab1d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303eb7923a91dcecc2d9bc1133d5c5d.png)
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3 . 如图,P为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0ac188b55d6377c0ab00a28f3b9296.png)
上的动点,过P作椭圆
的切线交圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780231ff0af68a65a3d740a2c858b26.png)
于M,N,过M,N作
切线交于Q,则Q的轨迹方程为_______________ ;
的最大值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0ac188b55d6377c0ab00a28f3b9296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6992d4a7cfa2348894f7c991ed6171c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780231ff0af68a65a3d740a2c858b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95f1a8e66ddfb0277c3efb15bf8b7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9902b08a6e0aef5eac29c197a356320b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/de5896a5-8ca6-48a2-8ae5-bc88e615bf8e.png?resizew=219)
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4 . 已知抛物线C:
(p>0),过C的焦点F的直线
与抛物线交于A、B两点,当
⊥x轴时,|AB|=4.
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842695095574528/2927812091486208/STEM/1f767413c15748769d872c2d4ae759f4.png?resizew=199)
(1)求抛物线C的方程;
(2)如图,过点F的另一条直线
与C交于M、N两点,设
,
的斜率分别为
,
,若
(
),且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842695095574528/2927812091486208/STEM/1f767413c15748769d872c2d4ae759f4.png?resizew=199)
(1)求抛物线C的方程;
(2)如图,过点F的另一条直线
![](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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06744e0406608a46242aa6c2b194870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eec363212db572fbb9046aee21b4f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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2022-03-02更新
|
836次组卷
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7卷引用:四川省凉山州2021届高三二模数学(文科)试题
名校
解题方法
5 . 已知椭圆
的一个焦点为
,离心率为
,点P为圆
上任意一点,
为坐标原点.
(1)记线段OP与椭圆C的交点为Q,求
的取值范围;
(2)设直线l经过点P,且与椭圆C相切,与圆M相交于另一点A,点A关于原点的对称点为B,试判断直线PB与椭圆C的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b7ac31193004dcb7a71e8f657ad897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5f931d7a4bb4b9f7265f200248bac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)记线段OP与椭圆C的交点为Q,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b1113864968119e61aeee9ba9c613b.png)
(2)设直线l经过点P,且与椭圆C相切,与圆M相交于另一点A,点A关于原点的对称点为B,试判断直线PB与椭圆C的位置关系,并证明你的结论.
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6 . 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
|
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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)
7 . 1.线段
的长等于3,两端点Q、R分别在x轴和y轴上滑动,点S在线段QR上,且
,点S的轨迹为曲线C.
(1)求曲线C的方程
(2)曲线C与x轴相交于A、B两点,P为曲线C上一动点,直线PA,PB与直线
交于M,N两点,
与
的外接圆的周长分别为
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a573cc3f99b684f932c517bc822135d2.png)
(1)求曲线C的方程
(2)曲线C与x轴相交于A、B两点,P为曲线C上一动点,直线PA,PB与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f882ff9e3447c6966660326535aed9f.png)
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2021-11-12更新
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7卷引用:四川省成都市树德中学2021届高三高考适应性考试数学(文)试题
四川省成都市树德中学2021届高三高考适应性考试数学(文)试题四川省成都市树德中学2021届高三高考适应性考试数学(理)试题新疆喀什市部分学校2022届高三全真模拟数学试题(已下线)专题07 不等式与线性规划-备战2022年高考数学(文)母题题源解密(全国乙卷)(已下线)考点38 椭圆-备战2022年高考数学典型试题解读与变式(已下线)考点42 圆锥曲线中的范围与最值问题-备战2022年高考数学典型试题解读与变式(已下线)专题26 圆锥曲线(理科)解答题20题-备战2022年高考数学冲刺横向强化精练精讲
名校
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8 . 已知双曲线
的一个焦点为
,且经过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567918889924d7023b02560b27ea88a6.png)
(1)求双曲线C的标准方程;
(2)已知点A是C上一定点,过点
的动直线与双曲线C交于P,Q两点,若
为定值
,求点A的坐标及实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b707fdf035eb2fb4467958893c60381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567918889924d7023b02560b27ea88a6.png)
(1)求双曲线C的标准方程;
(2)已知点A是C上一定点,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b54b9cf95418bc3dce6e4c698b9907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd2cb1ab5832099dae673132f7c56cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2021-10-06更新
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1549次组卷
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5卷引用:四川省广安市岳池县2021-2022学年高二上学期期中考试数学(理)试题
四川省广安市岳池县2021-2022学年高二上学期期中考试数学(理)试题广东省珠海市2022届高三上学期9月摸底测试数学试题福建省晋江市第一中学2022届高三上学期第三次阶段考数学试题(已下线)9.6 三定问题及最值(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)一轮复习大题专练66—双曲线2—2022届高三数学一轮复习
9 . 已知抛物线
的焦点为
.且
与圆
上点的距离的最小值为
.
(1)求抛物线的方程;
(2)若点
在圆
上,
,
是
的两条切线.
,
是切点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50b56744124be98d9bd7988c18c412f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求抛物线的方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/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/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2021-09-29更新
|
1799次组卷
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9卷引用:四川省成都市树德中学2021-2022学年高三上学期入学考试文科数学试题
四川省成都市树德中学2021-2022学年高三上学期入学考试文科数学试题四川省成都市树德中学2021-2022学年高三上学期入学考试理科数学试题四川省成都市青羊区树德中学2021-2022学年高三上学期数学(文)入学考试试题四川省成都市青羊区树德中学2021-2022学年高三上学期数学(理)入学考试试题黑龙江省大庆铁人中学2021-2022学年高二上学期期末考试数学试题四川省成都市简阳阳安中学2022-2023学年高三上学期开学考试数学(理)试题四川省达州外国语学校2024届高三上学期入学考试理科数学试题(已下线)专题42 盘点圆锥曲线中的面积问题——备战2022年高考数学二轮复习常考点专题突破(已下线)重难点10四种解析几何数学思想-2
名校
解题方法
10 . 已知椭圆
:
的左右焦点分别为
,左顶点为
,离心率为
,上顶点
,
的面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a127536a513fb5798a2807ed21b76848.png)
(1)求椭圆
的方程;
(2)设直线
:
与椭圆
相交于不同的两点
,
是线段
的中点.若经过点
的直线
与直线
垂直于点
,求
的取值范围.
![](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/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a127536a513fb5798a2807ed21b76848.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae077b198c3e6a891ca7c5eb6d53482a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790b9984af4b8765705507e5e83ea162.png)
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