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1 . 以下四个关于圆锥曲线的命题中:
①设
、
为两个定点,
为非零常数,若
,则动点
的轨迹为双曲线;
②过定圆
上一定点
作圆的动弦
,
为坐标原点,若
,则动点
的轨迹为椭圆;
③抛物线
的焦点坐标是
;
④曲线
与曲线
(
且
)有相同的焦点.
其中真命题的序号为______ 写出所有真命题的序号.
①设
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4562ddd51f544eaff300c9b4638646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②过定圆
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a6bb839093992d42c6c813c73ccad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
③抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315513892f06ef3ce82021d5e0566606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2762dfc22fc40385f211f1a23875424b.png)
④曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4e82ca0fbf98b8903c97467acd1d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69c2e4498e7916dbc05a71fc0c316ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5c9d9221866bca2fd57b9b31100c62.png)
其中真命题的序号为
您最近一年使用:0次
2021-08-26更新
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5卷引用:江西省景德镇一中2020-2021学年高一(1班)下学期期中考试数学试题
江西省景德镇一中2020-2021学年高一(1班)下学期期中考试数学试题(已下线)考点39 曲线与方程-备战2022年高考数学一轮复习考点帮(浙江专用)(已下线)专题6.2 期中押题检测卷(考试范围:第1-3章)2(中)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册) 河北省保定市唐县第一中学2021-2022学年高二上学期12月月考数学试题(已下线)解密15 双曲线方程(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(新高考专用)
名校
解题方法
2 . 已知曲线
.关于曲线W有四个结论:
①曲线W既是轴对称图形又是中心对称图形;
②曲线W的渐近线方程为
;
③当
时曲线W为双曲线,此时实轴长为2;
④当
时曲线W为双曲线,此时离心率为
.
则所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb65152906dd85d99319f2aa0b8e9fe.png)
①曲线W既是轴对称图形又是中心对称图形;
②曲线W的渐近线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba80160fe41b335cd9e54fd449f8387.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c328c9c4ec69c4275e27576fb61655.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c328c9c4ec69c4275e27576fb61655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7881094ce2f907c3aaf664318ecd3e2d.png)
则所有正确结论的序号为
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2024-01-26更新
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2卷引用:北京市通州区2023-2024学年高二上学期期末质量检测数学试卷
解题方法
3 . 已知三棱锥
中,
,
,
,
.关于该三棱锥有以下结论:①三棱锥
的表面积为
;②三棱锥
的内切球的半径
;③点
到平面
的距离为
;④若侧面
内的动点
到平面
的距离为
,且
,则动点
的轨迹为抛物线的一部分.其中正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9b8e7befcb7881c294070175b1a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00c750e915d7f9a7460970a4199071f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9641d01140939c44450bf39773272af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa37aefb6d45efe4e20ba48c2e7dfa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c966fa765420ae547f83e28dcc997a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266e095e1f7a31646992a5b7fac251d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.①② | B.③④ | C.① ②③ | D.①②③④ |
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4 . 卵圆是常见的一类曲线,已知一个卵圆
的方程为:
,
为坐标原点,点
,点
为卵圆上任意一点,有下列四种说法:①卵圆
关于
轴对称;②卵圆上不存在两点关于直线
对称;③线段
长度的取值范围是
;④
的面积最大值为1;
其中正确说法的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407e34a89e07e42932753c24f022cc43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
其中正确说法的序号是( )
A.①②③ | B.①③④ | C.②③④ | D.①②④ |
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5 . 心脏线,也称心形线,是一个圆上的固定一点在该圆绕着与其相切且半径相同的另外一个圆周滚动时所形成的轨迹,因其形状像心形而得名.心脏线的平面直角坐标方程可以表示为
,
,则关于这条曲线的下列说法:
①曲线关于
轴对称;
②当
时,曲线上有4个整点(横纵坐标均为整数的点);
③
越大,曲线围成的封闭图形的面积越大;
④与圆
始终有两个交点.
其中,所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f770bc2ebb38834deaa6f99e43b3f997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
①曲线关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
④与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244854b6b8c6e3b3f46ad4b53fa4017b.png)
其中,所有正确结论的序号是
您最近一年使用:0次
2022-01-12更新
|
779次组卷
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3卷引用:北京市房山区2021-2022学年高二上学期期末考试数学试题
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6 . 关于曲线C:
,给出下列说法:
①关于坐标轴对称; ②关于点
对称;
③关于直线
对称; ④是封闭图形,面积大于
.
则其中正确说法的序号是______
注:把你认为正确的序号都填上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b79ffef55f4609e7d23a888e508464.png)
![](https://img.xkw.com/dksih/QBM/2018/2/5/1875664405684224/1876385973739520/STEM/add361cc393c46f4a55b6ba72df6c7a7.png?resizew=6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
③关于直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
则其中正确说法的序号是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce8411079aca57f17d3ead32798f055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
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2卷引用:湖北省宜昌市第一中学2017-2018学年高二上学期期末考试数学(理)试题