名校
解题方法
1 . 已知双曲线
的一条渐近线方程
,原点到过
、
点的直线
的距离为
.
(1)求双曲线方程;
(2)过点
能否作直线
,使
与已知双曲线交于两点
、
,且
是线段
的中点?若存在,请求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bdeeb6f5e38e3464c357d00839a6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93eb996cb2d3a9cbe27e9fa1b38cfb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求双曲线方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a453aca6de44f9e23703ec8f421fa32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2022-12-09更新
|
412次组卷
|
4卷引用:重难点03圆锥曲线综合七种问题解题方法-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
(已下线)重难点03圆锥曲线综合七种问题解题方法-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)专题8.3 双曲线综合【九大题型】(举一反三)(新高考专用)-2上海市朱家角中学2021-2022学年高一下学期期末数学试题陕西省西安市周至县2024届高三一模数学(理)试题
2 . 双曲线
的左、右顶点分别为
,
,过点
且垂直于
轴的直线
与该双曲线
交于点
,
,设直线
的斜率为
,直线
的斜率为
.
(1)求曲线
的方程;
(2)动点
,
在曲线
上,已知点
,直线
,
分别与
轴相交的两点关于原点对称,点
在直线
上,
,证明:存在定点
,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f5d9add1a8ef4d5d520f9bcc568d42.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/269a51e0f77f63bae2df3dc8b1d4f455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7219ba6e1a9dfe3f11dc3462be1a9fd.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)动点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de78b493bc2cc9696c584325c22ee7.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7555f635da615b09b7e2f08ddbeaf1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eebe4d3c925e04eb4a5e0318143482fb.png)
您最近一年使用:0次
2022-11-25更新
|
967次组卷
|
5卷引用:专题9-2 圆锥曲线(解答题)-1
2023高三·全国·专题练习
名校
解题方法
3 . 已知
,
,点
满足
,记点
的轨迹为
,
(1)求轨迹
的方程;
(2)若直线
过点
且法向量为
,直线与轨迹
交于
、
两点.
①过
、
作
轴的垂线
、
,垂足分别为
、
,记
,试确定
的取值范围;
②在
轴上是否存在定点
,无论直线
绕点
怎样转动,使
恒成立?如果存在,求出定点
;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4e568d9cd57c442f011a787ab8aaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c2124260496e9307d6448c0c943f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150284ac8349a939d64b08e706365839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462cad129b775ffac3f15ffe45741286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
①过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.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/0fa6b5a04f3a62b18c4b00442ccf9c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
②在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6473a6a934c3111564dc1888be05ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2022-11-22更新
|
1597次组卷
|
3卷引用:专题34 圆锥曲线存在性问题的探究
4 . 已知双曲线
与椭圆
有相同的焦点,且焦点到渐近线的距离为2.
(1)求双曲线
的标准方程;
(2)设
为双曲线
的右顶点,直线
与双曲线
交于不同于
的
,
两点,若以
为直径的圆经过点
且
于
,证明:存在定点
,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6205da5e1d2730ee0b3de8bca3e29f5e.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce50eeb654ef50f36a582c785f273ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803a617fb53e67edbc2955cb629c329b.png)
您最近一年使用:0次
2022-11-13更新
|
990次组卷
|
5卷引用:专题16圆锥曲线(解答题)
(已下线)专题16圆锥曲线(解答题)(已下线)模块八 专题9 以解析几何为背景的压轴解答题山西省晋城市第一中学校2022-2023学年高二上学期11月月考数学试题贵州省2022-2023学年高二上学期期中联合考试数学试题黑龙江省大庆市2023届高三第一次教学质量检测数学试题
5 . 已知双曲线
,过点
的动直线与C交于两点P,Q,若曲线C上存在某定点A使得
为定值
,则
的值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4058fc45c49e6710ba7e273cb7888704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29610a3415c1e795d35979a5a9ff69f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898c77f9f02cb8bad38f37a5ef4a22b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7043c5176a2673360277467c88198e1.png)
您最近一年使用:0次
2022-11-10更新
|
740次组卷
|
4卷引用:重难专攻(九)?圆锥曲线中的定值问题 讲
(已下线)重难专攻(九)?圆锥曲线中的定值问题 讲(已下线)专题03 圆锥曲线中的定点定值问题(两大题型)浙江省杭州市2022-2023学年高三上学期期中数学试题山西省太原市第五中学校2023届高三上学期期末数学试题
名校
解题方法
6 . 已知双曲线
的右焦点
到渐近线的距离为
.
(1)求双曲线
的方程.
(2)过点
的直线与双曲线
的右支交于
两点,在
轴上是否存在点
,使得点
到直线
的距离相等? 若存在,求出点
的坐标; 若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db3b46f0bf8897318fb3d0114e56e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求双曲线
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2022-10-27更新
|
1401次组卷
|
12卷引用:第04讲 圆锥曲线综合(练)
(已下线)第04讲 圆锥曲线综合(练)河南省创新发展联盟2022-2023学年高二上学期第二次联考(期中)数学试题山西省三晋名校联盟2023届高三上学期阶段性(二)数学试题山西省忻州市2023届高三上学期10月联考数学试题甘肃省兰州市兰州西北中学2022-2023学年高三上学期期中数学(理科)试题辽宁省大连市第十五中学2022-2023学年高二上学期期中数学试题甘肃省兰州市第二中学2022-2023学年高三上学期第二次月考文科数学试题河北省沧衡八校联盟2022-2023学年高三上学期11月期中考试数学试题新疆维吾尔自治区喀什地区疏附县2022-2023学年高二上学期11月期中数学试题湖南省部分学校2022-2023学年高三上学期10月联考数学试题广东省多校2023届高三上学期10月联考数学试题湖南省湘潭市第一中学2022-2023学年高三上学期期中数学试题
名校
解题方法
7 . 已知双曲线
经过点
,两条渐近线的夹角为
,直线
交双曲线于
两点.
(1)求双曲线
的方程.
(2)若动直线
经过双曲线的右焦点
,是否存在
轴上的定点
,使得以线段
为直径的圆恒过
点?若存在,求实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd0c50bcc9df1beefb6d160408019c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951c5201d4cfe9d71967d54c037dc2d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d256d7276759d722bf88e373a71e9f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(2)若动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f6ea2db082eed0a0f3e21764c5ba97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
您最近一年使用:0次
2022-10-22更新
|
2413次组卷
|
9卷引用:专题19 圆锥曲线(讲义)-2
8 . 已知双曲线
的左焦点坐标为
,直线
与双曲线
交于
两点,线段
中点为
.
(1)求双曲线
的方程;
(2)经过点
与
轴不重合的直线
与双曲线
交于两个不同点
,点
,直线
与双曲线
分别交于另一点
.
①若直线
与直线
的斜率都存在,并分别设为
.是否存在实常数
,使得
?若存在,求出
的值;若不存在,请说明理由.
②证明:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5210e562b5a82e12c76d48910a656224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b818c643aa48668eabc47a79e8eca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec2ddb5af2259e125872e0b0e32ee8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f78464fbd81cdda9febcefb5252566a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b09e2d46f94b9ca3caf3f8283619c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c4a70b6a022a1edb45482d8335ce68.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67300207553ae70b997bde84ca730cf8.png)
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6fdb50dcd92eae8b7e19e5a52147b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f78464fbd81cdda9febcefb5252566a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2896fdcb5b81aee8ca7b49ffce40626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ddab1ca2e7187211d0d2bdfbfb54aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67300207553ae70b997bde84ca730cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422cbf74078aaee2e59fce1cbe25be27.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80861c13bb2d470a2953bebc5e3ea044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9faeed172ec5b88966b0d1c52748d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3360ca70819ab78d02e1cfa01d51d56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9faeed172ec5b88966b0d1c52748d41.png)
②证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2022-10-18更新
|
1365次组卷
|
6卷引用:第04讲 圆锥曲线综合(练)
(已下线)第04讲 圆锥曲线综合(练)(已下线)专题9-5 圆锥曲线大题基础:定点归类(已下线)专题08 椭圆双曲线综合大题(9题型)-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)(已下线)专题7-4圆锥曲线五个方程型大题归类-1重庆市第一中学校2022-2023学年高二上学期10月月考数学试题重庆市南开中学校2022-2023学年高二上学期11月月考数学试题
9 . 已知双曲线
和点
.
(1)斜率为
且过原点的直线与双曲线
交于
两点,求
最小时
的值.
(2)过点
的动直线与双曲线
交于
两点,若曲线
上存在定点
,使
为定值
,求点
的坐标及实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4058fc45c49e6710ba7e273cb7888704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
(1)斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb65bee4fb8c2cbdd36e318cd652f928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)过点
![](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/f6bce3d91ca23b86d8c6625f2632e437.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/fbd2cb1ab5832099dae673132f7c56cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
10 . 已知双曲线C:
经过点(2,3),两条渐近线的夹角为60°,直线l交双曲线于A、B两点.
(1)求双曲线C的方程.
(2)若l过原点,P为双曲线上异于A、B的一点,且直线PA、PB的斜率
、
均存在.求证:
为定值.
(3)若l过双曲线的右焦点
,是否存在x轴上的点M(m,0),使得直线l绕点
无论怎样转动,都有
成立?若存在,求实数m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
(1)求双曲线C的方程.
(2)若l过原点,P为双曲线上异于A、B的一点,且直线PA、PB的斜率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9626bd07f966ea26a51dcd8ceba04ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf32f4d595c02a8c0f7cc5f8fd0c931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc157c66eef6affd86e48432176c4240.png)
(3)若l过双曲线的右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89509122e62ab0f9e7fef2158f30b7b4.png)
您最近一年使用:0次
2022-09-08更新
|
1092次组卷
|
16卷引用:高考新题型-圆锥曲线
高考新题型-圆锥曲线(已下线)专题08 椭圆双曲线综合大题(9题型)-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)(已下线)专题3-4 双曲线大题综合10种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)上海市曹杨二中2018-2019学年高二下学期期中数学试题上海市上海师范大学附属外国语中学2018-2019学年高二上学期期末数学试题上海市延安中学2018-2019学年高三上学期9月月考数学试题湖南省长沙市明德中学2019-2020学年高二上学期12月月考数学试卷2017年上海市松江区高考一模数学试题上海市七宝中学2021届高三上学期摸底数学试题苏教版(2019) 选修第一册 突围者 第3章 专项拓展训练3 与圆锥曲线有关的定点、定值问题沪教版(2020) 选修第一册 精准辅导 第2章 2.3(3) 双曲线的性质(第2课时)河南省洛阳市栾川县第一高级中学2022-2023学年高三下学期入学测试数学试题(已下线)3.3(附加3)圆锥曲线定点与定值问题-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)江苏省无锡市南菁高级中学2020-2021学年高二上学期(强化班)期中数学试题(已下线)专题27 《圆锥曲线与方程》中的夹角角度问题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) (已下线)第6课时 课中 直线与双曲线的位置关系