名校
解题方法
1 . 已知双曲线:
,点M为双曲线C右支上一点,A、B为双曲线C的左、右顶点,直线
与y轴交于点D,点Q在x轴正半轴上,点E在y轴上.
(1)若点
,
,过点Q作BM的垂线l交该双曲线C于S,T两点,求
的面积;
(2)若点M不与B重合,从下面①②③中选取两个作为条件,证明另外一个成立.①
;②
;③
.注:若选择不同的组合分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d977e5d0854905f7bbe2a74c9b2e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c441c7e1d4bc397894cc8a6a169e0d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17713b33d9847c01770ff6873efb8d3.png)
(2)若点M不与B重合,从下面①②③中选取两个作为条件,证明另外一个成立.①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6049e763beac1c5aa60da1ec85edeaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270a7262986930a105301af8e33e55f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ebfd148b89a580e3ac7d68c70b64dd.png)
您最近一年使用:0次
2023-04-20更新
|
2669次组卷
|
6卷引用:广东省深圳市2023届高三二模数学试题
广东省深圳市2023届高三二模数学试题福建省厦门第一中学2023届高三下学期4月期中考试数学试题(已下线)模块四 专题7 解析几何(已下线)专题06 解析几何(已下线)押新高考第21题 圆锥曲线(已下线)技巧04 结构不良问题解题策略(5大核心考点)(讲义)
真题
解题方法
2 . 已知双曲线
左右顶点分别为
,过点
的直线
交双曲线
于
两点.
(1)若离心率
时,求
的值.
(2)若
为等腰三角形时,且点
在第一象限,求点
的坐标.
(3)连接
并延长,交双曲线
于点
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a3c16c6fb4a254b44936b2caf107a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8547f2b4e89b0ae1445bda02d46f0668.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/f6bce3d91ca23b86d8c6625f2632e437.png)
(1)若离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0276541c12707b24d2f06ea3d976cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f02a5f7c7bed4e46a9ea36b510590a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d353f7781e779b5c72e56388934e345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
3 . 已知双曲线
的左、右焦点分别为
、
,过坐标原点
的直线与双曲线
交于
两点,点
为双曲线
上异于
的一动点,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de66df5b4cd1344339588b99bf7214a4.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
A.![]() |
B.若以![]() ![]() ![]() |
C.若![]() ![]() |
D.设![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-03-24更新
|
2201次组卷
|
7卷引用:河北省石家庄市2021-2022学年高二上学期期末数学试题
河北省石家庄市2021-2022学年高二上学期期末数学试题(已下线)高二数学下学期期末全真模拟卷(1)(考试范围:高中全部内容)-2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)11.5 圆锥曲线专项训练河北省辛集市2022-2023学年高二上学期期末数学试题(已下线)模块五 倒数第5天 圆锥曲线(已下线)第12讲 双曲线(5大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)黑龙江省双鸭山市第一中学2023-2024学年高二上学期12月月考数学试题
名校
4 . 已知平面上到定点
的距离与到定直线
:
的距离之比为常数
的点的轨迹为曲线
.
(1)求曲线
的方程;
(2)把曲线
及直线
都向左平移5个单位长度,得到曲线
及直线
,写出
及
的方程(只写出结果);
(3)若
,
是
上的两点,且
.直线
交直线
于点
,求直线
与直线
所成锐角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1d8736a2f5a41c1942f8684ab3a81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35254a53dabcf0e63e437774ceaf417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)把曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(3)若
![](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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660964e4c6710e01ba34521ad419c3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963111aff6952322dfaca75ae069873c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
您最近一年使用:0次
解题方法
5 . 已知双曲线C:
,
,
为C的左、右焦点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.双曲线![]() |
B.若P为C上一点,且![]() ![]() ![]() |
C.若直线![]() ![]() ![]() |
D.在C的左、右两支上分别存在点M,N使得![]() |
您最近一年使用:0次
名校
6 . 设直线
,点A和点B分别在直线
和
上运动,且
(其中O为坐标原点).
(1)求AB的中点T的轨迹方程C:
(2)是否存在直线
满足直线l与(1)中的曲线C交于M,N两点,且以MN为直径的圆经过曲线C的右焦点?若存在,求出k,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468f9bff2849dd9f0189717529f8ef0f.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/cfae5e4027c406c3eb027d5f3c05dca9.png)
(1)求AB的中点T的轨迹方程C:
(2)是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
您最近一年使用:0次
名校
解题方法
7 . 已知双曲线
是其左、右两个焦点.
是位于双曲线
右支上一点,平面内还存在
满足
.
(1)若
的坐标为
,求
的值;
(2)若
,且
,试判断
是否位于双曲线上,并说明理由;
(3)若
位于双曲线上,试用
表示
,并求出
时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617a0ed534872c16e9b94a3c8c22b4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f3eec7cd6fe8711473cec22429ab10.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f903df30afd0fd8750c5d2773b6df62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b06a24dc3e61aaee1d1864c429eab4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab709df84f0dd79fd55d58bcab888676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1961edd7f0ba14ba9afc074964c2b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd95d105e2f0b8a960761271fc893d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1961edd7f0ba14ba9afc074964c2b3.png)
您最近一年使用:0次
2022-06-11更新
|
1433次组卷
|
6卷引用:上海市光明中学2022届高三模拟(一)数学试题
上海市光明中学2022届高三模拟(一)数学试题(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点3 圆锥曲线中的存在性、探索性问题综合训练(已下线)专题12平面解析几何必考题型分类训练-4(已下线)专题19 圆锥曲线 (模拟练)-2(已下线)单元提升卷10 平面解析几何2022届上海市普通高等学校招生全国统一考试数学模拟试题(一)
解题方法
8 . 设双曲线
的中心在坐标原点
,焦点在
轴上,
的顶点
在
轴上,顶点
在
的左支上,直线
分别与
的右支交于
两点,若
,且
,则
的渐近线方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](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/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](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/575bced0e4287196b95b20ef7500711c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1f0d3cca6e82ecd4b933e0de3df9a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0667dd596536ce78518d0de10f6b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
解题方法
9 . 如图,正六边形
的边长为2.已知双曲线
的焦点为A,D,两条渐近线分别为直线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/d26a31c2-bf8a-4792-ab01-6a37f286b836.png?resizew=142)
(1)建立适当的平面直角坐标系,求
的方程;
(2)过A的直线l与
交于M,N两点,
,若点P满足
,证明:P在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/d26a31c2-bf8a-4792-ab01-6a37f286b836.png?resizew=142)
(1)建立适当的平面直角坐标系,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)过A的直线l与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b599867e80a7bbc57303c5f2bb1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b86edc0c4934a2d38d94b1e862b563.png)
您最近一年使用:0次
2023-03-07更新
|
638次组卷
|
2卷引用:福建省莆田市2023届高三下学期3月第二次教学质量检测数学试题
10 . 在直角坐标系
中,
是双曲线
的两条渐近线上的动点,满足点A在第一象限,点
在第四象限,且直线
与
的右支有交点.
(1)求
的最小值;
(2)设
是直线
与
的一个交点且
.记
上的点到
的焦点的距离的取值集合为S,若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da8a341058083ab6ee318b4107b43da.png)
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