1 . 已知双曲线
的渐近线为
,双曲线
与双曲线C的渐近线相同,过双曲线
的右顶点的直线与
,在第一、四象限围成三角形面积的最小值为8.
(1)求双曲线
的方程;
(2)点P是双曲线
上任意一点,过点P作
依次与双曲线C和
交于A,B两点,再过点P作
依次与双曲线C和
交于E,F两点,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(2)点P是双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca086092226075eb257f10f674eed9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49ac3a8f9f4f495cbc7629eb7c855b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2868ec4ce76288fe9b77247f4f467f6.png)
您最近一年使用:0次
2 . 已知直线
,
,动点
满足
,且到
和
的距离之积为
.
(1)求
的轨迹
的方程;
(2)已知
,过
的动直线
与
交于不同两点
,
,若线段
上有一点
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b65826e98ba9bea060a68b4a66a2555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41bd9a29a1bde0ab8d008769bfd279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55307ac4f2f3cd3b60bdf21c533290e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145ac6e6a9f66364d9ea317c4f520561.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/7294f5ae2a24ff42e84cd9773b2a7287.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd94711b2807dce4e05fe4c4ec52cdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b83a835c3401602a384a0a6834f128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7b401c07843a08cfdfb63ac53b32ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6d8fc78832b4b7286be49de6378120.png)
您最近一年使用:0次
3 . 已知双曲线H:
的左、右焦点为
,
,左、右顶点为
,
,椭圆E以
,
为焦点,以
为长轴.
(1)求椭圆E的离心率;
(2)设椭圆E交y轴于
,
,过
的直线l交双曲线H的左、右两支于C,D两点,求
面积的最小值;
(3)设点
满足
.过M且与双曲线H的渐近线平行的两直线分别交H于点P,Q.过M且与PQ平行的直线交H的渐近线于点S,T.证明:
为定值,并求出此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](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/643ef7d761de0e794fc39937dc72ac6a.png)
(1)求椭圆E的离心率;
(2)设椭圆E交y轴于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f2baab31438ea8290e1a309e74a187.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e0db273061d0331e4e5da9ff1e955e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c689487de9876b59e1f14a0c4140ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b5bdfe08a7bb88aab89d65ff01863c.png)
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4 . 平面直角坐标系
中,
为动点,
与直线
垂直,垂足
位于第一象限,
与直线
垂直,垂足
位于第四象限,
且
,记动点
的轨迹为
.
(1)求
的方程;
(2)已知点
,
,设点
与点
关于原点
对称,
的角平分线为直线
,过点
作
的垂线,垂足为
,交
于另一点
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8660c00328e6a398de20d82846f963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd85a2db359624bf56acb372ea3c1fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61e15e2a1d984933f47d23327ed375a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88167966e441d533565130507f6d585c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8547f2b4e89b0ae1445bda02d46f0668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e258dc5c8b4ea30bca80a56098065402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ef056105bb8c33072bb13858639162.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5471ed6b678bdaa491d65e34f2ee782e.png)
您最近一年使用:0次
解题方法
5 . 已知双曲线
的离心率为2,右焦点
到渐近线的距离为
.
(1)求双曲线的标准方程;
(2)若点
为双曲线右支上一动点,过点
与双曲线相切的直线
,直线
与双曲线的渐近线分别交于M,N两点,求
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9661f922ba80f0b26782ce7b176ec8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求双曲线的标准方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/ecfb02e157819a2bdd0f2790cbc825e9.png)
您最近一年使用:0次
6 . 已知双曲线
的一条渐近线方程的倾斜角为
,焦距为4.
(1)求双曲线
的标准方程;
(2)A为双曲线
的右顶点,
为双曲线
上异于点A的两点,且
.
①证明:直线
过定点;
②若
在双曲线的同一支上,求
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)A为双曲线
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59747cee312ee5140643428cae79efa.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
您最近一年使用:0次
2023-09-12更新
|
784次组卷
|
3卷引用:河南省周口市项城市2022-2023学年高二下学期期中数学试题
河南省周口市项城市2022-2023学年高二下学期期中数学试题山东省济宁市第一中学2023-2024学年高二上学期质量检测(三)数学试题(已下线)第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)
名校
解题方法
7 . 已知双曲线
的离心率为
,且焦点到渐近线的距离为1,
为双曲线上任意一点(
),过点
的直线与圆
相切于
两点
(1)求双曲线的标准方程
(2)求点
所在的直线方程
(3)双曲线是否存在点
,
,使得
的面积最大,若存在求出点
的坐标,及
的最大面积,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528a243eb93f63c1e126409be1fb3fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21872d8f6a518e0a2993ccf7a795ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a1bc7e5b5d807bdff0cb24584f0e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求双曲线的标准方程
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(3)双曲线是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21872d8f6a518e0a2993ccf7a795ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a1bc7e5b5d807bdff0cb24584f0e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,已知椭圆
与等轴双曲线
共顶点
,过椭圆
上一点P(2,-1)作两直线与椭圆
相交于相异的两点A,B,直线PA、PB的倾斜角互补,直线AB与x,y轴正半轴相交,分别记交点为M,N.
(2)若直线AB与双曲线
的左,右两支分别交于Q,R,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e6314e24c0225d455415c52124052b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04c8d7fbd6165d240cad25eaef7b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若直线AB与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fbac86947f24d80503333eed69e0427.png)
您最近一年使用:0次
2023-01-02更新
|
1330次组卷
|
2卷引用:湖南省长沙市雅礼中学2022-2023学年高三上学期月考(五)数学试题
解题方法
9 . 已知
,
为双曲线E:
(
,
)的左右焦点,点
在双曲线E上,O为坐标原点.
(1)求双曲线E的标准方程;
(2)若不与坐标轴平行的动直线l与双曲线E相切,分别过点
,
作直线l的垂线,垂足为P,Q,求
面积最大值.
![](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/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/3f8ba2b1920103e0879cff3de727a90c.png)
(1)求双曲线E的标准方程;
(2)若不与坐标轴平行的动直线l与双曲线E相切,分别过点
![](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/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
您最近一年使用:0次
2022·全国·模拟预测
10 . 已知双曲线E:
的左、右顶点分别为A,B,且
,过原点O的直线l与双曲线E相交于不同的两点C,D,且
.
(1)求双曲线E的标准方程;
(2)设点P是双曲线E的右支上一点,过点P的直线m与双曲线E的两条渐近线分别交于点
,
,其中
,若
,且
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef046167223338a8dd88109dbb9f9503.png)
(1)求双曲线E的标准方程;
(2)设点P是双曲线E的右支上一点,过点P的直线m与双曲线E的两条渐近线分别交于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
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