解题方法
1 . 已知中心在坐标原点
,焦点在
轴上的双曲线
的焦距为4,且过点
.
(1)求双曲线
的标准方程;
(2)过点
的直线
交双曲线
的右支于
,
两点,连接
并延长交双曲线
的左支于点
,求
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472335b39f337e413a4d8e90d1d6a3d9.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/a812a9b58ccba331cfd21d244329af01.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次
名校
2 . 已知函数
是偶函数,当
时,
,则曲线
在
处的切线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fda303d541981d7f1231c870e2462b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-02-16更新
|
1404次组卷
|
4卷引用:四川省成都市石室中学2024届高三上学期期末数学(理)试题
四川省成都市石室中学2024届高三上学期期末数学(理)试题四川省成都市石室中学2024届高三上学期期末数学(文)试题(已下线)5.2.1+5.2.2+5.2.3导数运算 第三练 能力提升拔高(已下线)广东省佛山市2024届高三教学质量检测(一)数学试题变式题1-6
名校
解题方法
3 . 下列叙述错误的是( )
A.命题“![]() ![]() ![]() ![]() |
B.若幂函数![]() ![]() ![]() ![]() |
C.![]() ![]() |
D.设![]() ![]() ![]() |
您最近一年使用:0次
2024-02-15更新
|
470次组卷
|
2卷引用:四川省成都市树德中学2024届高三上学期期末数学(理)试题
4 . 已知椭圆
:
的左、右焦点分别为
,
,上顶点为
,
到直线
的距离为
,且
.
(1)求椭圆
的标准方程;
(2)过
的直线m与椭圆
交于
两点,过
且与m垂直的直线n与圆O:
交于C,D两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e345142d3e746168664cf54edcd9b4d7.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a905c6fdf31080227d0f82a3080f3d4.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4503fcbaca90a4acc6a714bcbda9c8fa.png)
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解题方法
5 . 如图,圆O的半径为2,A是圆内一个定点,且
,B是圆外一个定点,且
,P是圆O上任意一点.线段
的垂直平分线
和半径
相交于点Q,线段
的垂直平分线
和半径OP相交于点R,当点在圆上运动时,点Q和点R的运动轨迹分别是椭圆和双曲线,设它们的离心率分别为
和
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ed6e21185ce4b8eadc7c807806bde5.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95b221648e1af2e931e72b323290b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552c8560b9790cd2349e340b522a3be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0101a7b5c8a4aed0de2af363792e39a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ed6e21185ce4b8eadc7c807806bde5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/8662dbb7-f6a9-4abe-9e7b-3dd0a5136130.png?resizew=180)
您最近一年使用:0次
6 . 已知双曲线
的渐近线方程为
,点
在
上.
(1)求
的方程.
(2)设
是双曲线
的左顶点,过点
的直线
与
的右支交于
两点,直线
分别与直线
交于
两点.试探究:是否存在定点
,使得以
为直径的圆过点
?若存在求点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6bb019e2d7c6d17d15ec4d9043f5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3654254401fc902c3cb4912969f21f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.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/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa154ac33703b5c836047b2143697c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
7 . 已知
为椭圆
的右焦点,
分别为其左、右顶点,过点
作直线
与椭圆交于
两点(不与
重合),记直线
的斜率分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3d394a48e71a71c54319d51fe2c2f8.png)
(1)证明:
为定值
(2)若线段
的中点为
,过点
做垂直于
的直线交
轴于点
,试求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0b4bbfa0ed04cd3c2454d99d64e29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b0b3eff0713306d46971e01b4f820d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3d394a48e71a71c54319d51fe2c2f8.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275d213d7f338450e3fd9206fb9b174.png)
您最近一年使用:0次
8 . 已知点
在抛物线
上,斜率为
的直线与
交于
两点,记直线
的斜率分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
(1)证明:
为定值:
(2)若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f5d5c15db5be0ead8a86471573f1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53d223a09481973825c5e87ce2f5c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521002bec94a87a6699f17fbb9403fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499b1f470978c4f8cc05ffdebc2e961.png)
您最近一年使用:0次
23-24高二上·山东德州·期末
名校
解题方法
9 . 已知双曲线
的左、右焦点分别为
、
,点
在
上,点
在
轴上,
,
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4efa339dbb8c7026b0959971349ae18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f33922168fc98b736c163d4dc36b3d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-14更新
|
1686次组卷
|
5卷引用:四川省成都外国语学校2023-2024学年高三上学期期末考试理科数学试题
四川省成都外国语学校2023-2024学年高三上学期期末考试理科数学试题(已下线)山东省德州市2023-2024学年高二上学期期末考试数学试题湖南省2024年高三数学新改革提高训练三(九省联考题型)(已下线)黄金卷03(2024新题型)湖南省岳阳市2024届高三下学期考情信息卷数学试题
名校
10 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2561b06ec155ba6f6ecad767b02c555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffdde9fdb56d7ed688ca80086eb068cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2ad8d575603319e9ce65f3063a2168.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-02-14更新
|
1170次组卷
|
5卷引用:四川省成都外国语学校2023-2024学年高三上学期期末考试理科数学试题