1 . 已知实数
满足
,则点
的轨迹为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01aab7b1514944e7b349bc3596b8cd9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
A.抛物线 | B.双曲线 | C.一条直线 | D.两条直线 |
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2 . 已知抛物线
的顶点是坐标原点
,焦点是双曲线
的右顶点.
(1)求抛物线
的方程;
(2)若直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
与抛物线相交于A、B两点,解决下列问题:
(i)求弦长
;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f11a4314f30e0a5a7cfb2e290751fec.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
(i)求弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
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3 . 已知曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fbe5e9b0abbbaeccc641cee1b637c4.png)
,将曲线
用函数
表示,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fbe5e9b0abbbaeccc641cee1b637c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92da99f65ba23ab0ddcfd50d92b8ff31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() |
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4 . 已知
为坐标原点,抛物线
的焦点为
,过
的直线
与
交
,
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
A.![]() | B.若![]() ![]() ![]() |
C.若直线![]() ![]() | D.![]() |
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5 . 对称轴都在坐标轴上的双曲线过点
,
,斜率为
的直线
过点
.
(1)求双曲线的标准方程;
(2)若直线
与双曲线有两个交点,求斜率
的取值范围;
(3)是否存在实数
使得直线
与双曲线交于A,B两点,且点P恰好为AB中点?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3f986a4f053c576c8a58c7debc8829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b55968d5f6b29626b1303e3cfe3132f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd064fc631163ed5e461887aa53cf197.png)
(1)求双曲线的标准方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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6 . 已知双曲线
的左焦点为
,方向向量为
的直线l过
与双曲线左,右两支分别交于
,
两点且
,则双曲线离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fe34d47ef23e8884a5c0404e54ef54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/5c2e97d6fb41ec5eccfd1fe8f72a92a6.png)
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7 . 已知椭圆
:
的短轴长为
,且椭圆
经过点
.
(1)求椭圆
的方程;
(2)若过点
的直线与椭圆
相交于
,
两点,且
,求直线
的方程.
![](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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7950b79b4e43d650ca5d84e9fce65540.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23baf026a1dd9532845c195a428d8e76.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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2024-04-07更新
|
652次组卷
|
3卷引用:河南省洛阳市2023-2024学年高二上学期期末考试数学试题
解题方法
8 . 已知动圆过定点
,且在
轴上截得的弦
的长为
.
(1)求动圆圆心的轨迹
的方程;
(2)过轨迹
上一个定点
引它的两条弦
,
,若直线
,
的斜率存在,且直线
的斜率为
证明:直线
,
的倾斜角互补.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fd33efcd65204756e406f09afc1d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
(1)求动圆圆心的轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0f3f09c8548df28f59e124a795fd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6c23a3e22159ba8cf83c6c96e307fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d134204485637cd6bda21c8853df3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6c23a3e22159ba8cf83c6c96e307fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d134204485637cd6bda21c8853df3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4bab74b21722ce5f1d44a6e1de32b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba4e967df6e7bcff0f9f9843ffed15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6c23a3e22159ba8cf83c6c96e307fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d134204485637cd6bda21c8853df3c.png)
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2024-04-05更新
|
1000次组卷
|
2卷引用:江西省九江市六校2023-2024学年高二上学期期末联考数学试题
名校
解题方法
9 . 已知双曲线
的左焦点为
,过点
的直线
与
轴交于点
,与双曲线
交于点
(
在
轴右侧).若
是线段AF的中点,则双曲线
的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.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/9e07658d5c4dc4af5faa9d8370e3e6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.2 | C.![]() | D.3 |
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2024-03-31更新
|
574次组卷
|
3卷引用:四川省南充高级中学2023-2024学年高二下学期第一次月考(3月)数学试题
10 . 如图,已知正方体
的棱长为2,E,F分别是棱
的中点,点P为底面ABCD内(包括边界)的动点,则以下叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a438de4d260b84dfde7d0fd492b9c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/654b30f6-ad64-4531-bc60-9297ac712f5a.png?resizew=141)
A.存在点P,使得![]() ![]() |
B.若点P在线段CD上运动,则点P到直线BF的最近距离为![]() |
C.若点P到直线![]() |
D.若直线![]() ![]() |
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