2020高三·全国·专题练习
真题
解题方法
1 . (1)求右焦点坐标是
,且经过点
的椭圆的标准方程;
(2)已知椭圆
的方程是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
.设斜率为
的直线
,交椭圆
于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
两点,
的中点为
.证明:当直线
平行移动时,动点
在一条过原点的定直线上;
(3)利用(2)所揭示的椭圆几何性质,用作图方法找出下面给定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4b5304fcad9f2a5a355e26b2318f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b647d7e0213e12c73db1adb33e8a10d.png)
(2)已知椭圆
![](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/0faa2be655f8c6db5187a1928cf8bea9.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50312681cba520fc026f5b851c210d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)利用(2)所揭示的椭圆几何性质,用作图方法找出下面给定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/4d864af0-86dc-40c6-b710-7bd08bf0cf50.png?resizew=129)
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2020-05-26更新
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3卷引用:秒杀题型09 圆锥曲线中的中点弦-2020年高考数学试题调研之秒杀圆锥曲线压轴题
(已下线)秒杀题型09 圆锥曲线中的中点弦-2020年高考数学试题调研之秒杀圆锥曲线压轴题2005年普通高等学校春季招生考试数学试题(上海卷)沪教版(2020) 选修第一册 领航者 第2章 2.2椭圆 第2课时 椭圆的性质(1)
2 . (1)求右焦点坐标是
,且经过点
的椭圆的标准方程.
(2)已知椭圆
,设斜率为
的直线
交椭圆
于
两点,
的中点为
,证明:当直线
平行移动时,动点
在一条过原点的定直线上.
(3)利用(2)中所揭示的椭圆几何性质,用作图方法找出图中的定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/c28d9ef0eba44eeda5181dc7b083523c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/d8e5e6ac67eb4145853c8cf83a5f9119.png)
(2)已知椭圆
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/7477185b1fe941e981b8590cdca860b1.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/1f22135cfb4d452e8f4ff5c0ea89c38a.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/6966e45b096d44088b1f951176c7fe24.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/da9e63efc9b9427ca212f9b6cadd87f1.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/a101441825324af9bc98161496aa0fdd.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/e62465c4941e4c3a8fc7bedf9dddda98.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/1d13f72b19fb4a32b9be6a541eab2263.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/6966e45b096d44088b1f951176c7fe24.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/1d13f72b19fb4a32b9be6a541eab2263.png)
(3)利用(2)中所揭示的椭圆几何性质,用作图方法找出图中的定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/82de281a98b141cc9bce4e539af0d4dc.png)
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3 . 一种画双曲线的工具如图所示,长杆OB通过O处的铰链与固定好的短杆OA连接,取一条定长的细绳,一端固定在点A,另一端固定在点B,套上铅笔(如图所示).作图时,使铅笔紧贴长杆OB,拉紧绳子,移动笔尖M(长杆OB绕O转动),画出的曲线即为双曲线的一部分.若|OA|=10,|OB|=12,细绳长为8,则所得双曲线的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/33da8c9a-b96d-4635-8914-658eeefbcca5.png?resizew=177)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/33da8c9a-b96d-4635-8914-658eeefbcca5.png?resizew=177)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-01-17更新
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6卷引用:【区级联考】北京市丰台区2019届高三第一学期期末考试数学(理)试题
【区级联考】北京市丰台区2019届高三第一学期期末考试数学(理)试题【市级联考】辽宁省沈阳市郊联体2019届高三第一次模拟考试数学(理科)试题苏教版(2019) 选修第一册 突围者 第3章 第二节 课时2 双曲线的几何性质(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) 北京交通大学附属中学2022届高三12月月考数学试题2023版 苏教版(2019) 选修第一册 突围者 第3章 第二节 课时2 双曲线的几何性质
名校
4 . 数学中有许多形状优美、寓意美好的曲线,曲线
就是其中之一.曲线C对应的图象如图所示,下列结论:
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
;
②曲线C与圆
有2个交点;
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:________ .(填写所有正确结论的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5a27e68ac82e560536b3bdefd4b08f.png)
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6274852e643a635e7340efa732edddc4.png)
②曲线C与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd89a03660c85fb78bd7fe82ee3068c.png)
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:
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3卷引用:贵州省六盘水市2019-2020学年高二下学期期末教学质量监测数学(理)试题
19-20高二·浙江·期末
解题方法
5 . 把椭圆
的短轴和焦点连线段中较长者、较短者分别作为椭圆
的长轴、短轴,使椭圆
变换成椭圆
,称之为椭圆的一次“压缩”.按上述定义把椭圆
“压缩”成椭圆
,得到一系列椭圆
,…当短轴长与焦距相等时终止“压缩”.经研究发现,某个椭圆
经过
次“压缩”后能终止,则椭圆
的离心率可能是①
,②
,③
,④
中的______ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b227b38b45b5fce63a6bdad8adf113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b227b38b45b5fce63a6bdad8adf113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6decaa352376a0689dffd773283fd1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde27c3cfe9b3e23077120ab684efd68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a809ca7fdd64561639655b464bdbc1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae0b861522b18be1753acc4474cbc9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607956aa6e6421c2a37570546887eec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
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6 . 已知点
的坐标分别是
,直线
相交于点
,且它们的斜率分别为
,下列命题是真命题的有____________ .(只填写序号)
①若
,则
的轨迹是椭圆(除去两个点)
②若
,则
的轨迹是抛物线(除去两个点)
③若
,则
的轨迹是双曲线(除去两个点)
④若
,则
的轨迹是一条直线(除去一点)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6917df35ab960d5958af89095219434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c8d6f4eb8d272265fe1ec25e1b8a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a690a05dc243e3c6736a6de514106ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7250bd16e71812ca4985abb14b27fccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
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7 . 下列结论:
(1)若
,则“
”成立的一个必要不充分条件是“
,且
”;
(2)存在
,且存在
使得
;
(3)若函数
的导函数是奇函数,则实数
;
(4)平面上的动点
到定点
的距离比
到
轴的距离大
的点
的轨迹方程为
;
(5)已知平面
满足
,则
;
(6)若
,则事件
与
是对立事件.
其中正确结论的序号为__________ .(填写所有正确的结论序号)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec124eb33e5ab4601b4b70f70913b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
(2)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ef778b8c90778644b6f34d2f851b0.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfe5f8a174b9b70fe067e171da7ea2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
(4)平面上的动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
(5)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3e3f7a929526d602d0a4010ba479a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cac3ca03e7640dceb04fbf33b8268b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
(6)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94cb714391a7e13d8e53bebd4042fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
其中正确结论的序号为
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8 . 平面直角坐标系中,
,
,若曲线
上存在一点
,使
,则称曲线
为“合作曲线”,有下列曲线①
;②
;③
;④
;⑤
,
其中“合作曲线”是__________ .(填写所有满足条件的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b47e7bf02b3ca16f7d96b9369e51a3.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/e5520bd24f656141b183ce10ce619873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28123e129b6426c9a5f31ad8ec2465b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f1596d3e260ec2198058d1b94ed7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87300fffa5f1a549a19222bf7ab14f3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16d1b1c4f6ae3b46ce8be922bf5186a.png)
其中“合作曲线”是
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3卷引用:河南省漯河市高级中学2018届高三上学期第三次模拟考试(期中)数学(文)试题
名校
9 . 平面直角坐标系
中,抛物线
的焦点为
,准线为
,过
的直线交抛物线于
两点,
于
,
于
,
中点为
,
于
,则下列说法:
①
为钝角三角形
②
为直角三角形
③
为钝角三角形
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fc9900588f71f30457f741feadd070.png)
正确命题的序号是__________ (填写你认为正确的所有命题的序号.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca717072d24c0e6fda2bb0d9c19b406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeba4806d9a03f7beb2f11d1d714bf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b282b8e3a04be2320c1f855b90cbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a9354a07397b21c33820fc2590e814.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6481f62501c45b1b5f163196fb29b5.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0a4aaef72dcd725367fa2aeb556b9c.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fc9900588f71f30457f741feadd070.png)
正确命题的序号是
您最近一年使用:0次
2018-01-15更新
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218次组卷
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2卷引用:黑龙江省哈尔滨市第三中学2017-2018届高二上学期模块考试(期末)文科数学试题
名校
10 . 有下列四种说法:
①命题“
”为假,则
、
至少一个为假;
②命题“一次函数都是单调函数”的否定是“一次函数都不是单调函数”;
③动点
到点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
与到点
的距离之和为2,则点
的轨迹是焦点在
轴上的椭圆;
④命题“若直线与双曲线相切,则该直线与双曲线只有一个公共点”的逆命题是真命题.
其中正确的有__________ .(填写序号)
①命题“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13472bf0353e16784a22e1f890fba40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
②命题“一次函数都是单调函数”的否定是“一次函数都不是单调函数”;
③动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4bc333cee094e9dd8f1f3ff86adc95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
④命题“若直线与双曲线相切,则该直线与双曲线只有一个公共点”的逆命题是真命题.
其中正确的有
您最近一年使用:0次