名校
解题方法
1 . 已知曲线
:
,点
,下面有四个结论:
①曲线
关于
轴对称;
②曲线
与
轴围成的封闭图形的面积不超过4;
③曲线
上任意点
满足
;
④曲线
与曲线
有5个不同的交点.
则其中所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e654afe0c08370274d854e1227f02e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce176fdfbb44b8459f441a8d805013f.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
③曲线
![](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/6a782979abb34633b027146eef128d9c.png)
④曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b0d4f1174ab593725c03e9245f687e.png)
则其中所有正确结论的序号是( )
A.①②③ | B.①②④ | C.①③④ | D.①②③④ |
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2 . 如果方程
所对应的曲线与函数
的图象完全重合,则如下结论正确的个数( )
①函数
是偶函数;
②
的图象上的点到坐标原点距离的最小值为1;
③函数
的值域为
;
④函数
有且只有一个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7352d1dc64802633b0409f6ff302ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c36c3781d5caf82f3749cd503d23ad6.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c534e240759d180cfd6aec100e501edd.png)
A.1 | B.2 | C.3 | D.4 |
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名校
解题方法
3 . 设点A,
,
的坐标分别为
,
,
,动点
满足:
,给出下列四个结论:
① 点P的轨迹方程为
;
②
;
③ 存在4个点P,使得
的面积为
;
④
.
则正确结论的个数是( )
![](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/dc30165c18de623d0a3efb961e606d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a5986ddebb9b8ea466beacc1523967.png)
① 点P的轨迹方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6d66601dad454b9cd96c972b3befec.png)
③ 存在4个点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ba9b58de88d84cf9eeb74c334846ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752036f0aea0ce1ee85f3283dd015b6c.png)
则正确结论的个数是( )
A.1 | B.2 | C.3 | D.4 |
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3卷引用:北京市北京师范大学附属中学2022-2023学年高二下学期期中考试数学试题
北京市北京师范大学附属中学2022-2023学年高二下学期期中考试数学试题北京高二专题01平面解析几何(已下线)专题13 椭圆的标准方程及几何性质(期末选择题13)-2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)
名校
解题方法
4 . 已知点
是曲线
(其中a,b为常数)上的一点,设M,N是直线
上任意两个不同的点,且
.则下列结论正确的是______ .
①当
时,方程
表示椭圆;
②当
时,方程
表示双曲线;
③当
,
,且
时,使得
是等腰直角三角形的点
有6个;
④当
,
,且
时,使得
是等腰直角三角形的点
有8个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296f6b73bcb1ea61bff5367a9a918613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef43a8e403c744851ebda3610ddd45.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296f6b73bcb1ea61bff5367a9a918613.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296f6b73bcb1ea61bff5367a9a918613.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ad03c9d3ac3b7cc9952979532b2415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a7551d073a061eef22c9e127d6deeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15a13b4190ac3d5feaee27a4c97b21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23b488f961d9fde37feb7f5c497c0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ad03c9d3ac3b7cc9952979532b2415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a7551d073a061eef22c9e127d6deeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0fed6f944ef4b07f7e33ca893581fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23b488f961d9fde37feb7f5c497c0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2卷引用:北京市东城区2022-2023学年高二上学期期末考试数学试题
解题方法
5 . 已知椭圆
:
(
)的离心率为
,长轴长与短轴长的和为6,
,
分别为椭圆
的左、右焦点.
(1)求椭圆
的方程;
(2)设
为椭圆
上一点,
.若
,
,
成等差数列,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef569668e797b1e94257fd5f4384dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0fdf344852f3e6162753bf2a00c7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fa27f8db6167d4802a510371077bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 设点
,
分别为椭圆
的左,右焦点,点P是椭圆C上任意一点,若使得
成立的点恰好是4个,则实数m的一个取值可以为( )
![](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/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f19ff9d533161dedf49cf9a921341.png)
A.0 | B.1 | C.2 | D.3 |
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|
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4卷引用:北京市十一学校2022-2023学年度高二上学期第一学段数学Ⅰ课程教与学诊断试题
7 . 已知椭圆C:
的一个焦点为
,离心率为
.点P为圆M:
上任意一点,O为坐标原点.
(1)求椭圆C的标准方程;
(2)记线段OP与椭圆C交点为Q,求
的取值范围;
(3)设直线l经过点P且与椭圆C相切,l与圆M相交于另一点A,点A关于原点O的对称点为B,试判断直线PB与椭圆C的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973aa6f1a268dbd02fa5236dc6f58647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c7f91f05a52da791a05d926adbab03.png)
(1)求椭圆C的标准方程;
(2)记线段OP与椭圆C交点为Q,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
(3)设直线l经过点P且与椭圆C相切,l与圆M相交于另一点A,点A关于原点O的对称点为B,试判断直线PB与椭圆C的位置关系,并证明你的结论.
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解题方法
8 . 已知曲线
,以下关于曲线C的结论正确的个数为( )
①曲线C关于
轴对称
②曲线C上有且仅有3个整点(整点指横纵坐标均为整数的点)
③曲线C上一点P满足
(
为坐标原点)
③曲线C上与图形
有且仅有两个公共点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121070e738b6218249a964e3b4d80262.png)
①曲线C关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②曲线C上有且仅有3个整点(整点指横纵坐标均为整数的点)
③曲线C上一点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c43a4782cfbeb91fa261adc48c4761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
③曲线C上与图形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479cd7c32b15b8b19fd6eb358c4e6cc.png)
A.1 | B.2 | C.3 | D.4 |
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9 . 已知
为椭圆
上一点,
为椭圆长轴上一点,
为坐标原点.给出下列结论:
① 存在点
,
,使得 △
为等边三角形;
② 不存在点
,
,使得 △
为等边三角形;
③存在点
,
,使得
;
④不存在点
,
,使得
.
其中,所有正确结论的序号是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
① 存在点
![](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/3e17dc84ba2e871aeb3a3fd2a2b5f1a8.png)
② 不存在点
![](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/3e17dc84ba2e871aeb3a3fd2a2b5f1a8.png)
③存在点
![](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/854fe0471f3f3649a72121bc3afbb93f.png)
④不存在点
![](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/854fe0471f3f3649a72121bc3afbb93f.png)
其中,所有正确结论的序号是
您最近一年使用:0次
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4卷引用:北京市西城区北京师范大学第二附属中学2021-2022学年高二上学期期中数学试题
21-22高三上·北京·阶段练习
名校
10 . 若
是椭圆
的一个焦点,
是该椭圆上的动点,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb54c4990f7725e9fb6ae5ad3ddd732c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-10-26更新
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7卷引用:北京丰台二中2022届高三10月月考数学试题
(已下线)北京丰台二中2022届高三10月月考数学试题(已下线)专题19 圆锥曲线-2022年高考数学一轮复习小题多维练(新高考版)四川省成都外国语学校2021-2022学年高二上学期期中考试文科数学试题江苏省盐城市大丰区新丰中学2021-2022学年高二上学期期中数学试题(已下线)解密18 椭圆(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(全国通用)(已下线)专题3.4 椭圆的简单几何性质-重难点题型检测-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)期中押题预测卷(考试范围:第1-3章)(拔高卷)-【单元测试】2022-2023学年高二数学分层训练AB卷(苏教版2019选择性必修第一册)