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)
您最近一年使用:0次
2020-05-26更新
|
483次组卷
|
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)
13-14高二下·上海金山·期末
2 . 下图是利用计算机作图软件在直角坐标平面
上绘制的一列抛物线和一列直线,在焦点为
的抛物线列
中,
是首项和公比都为
的等比数列,过
作斜率2的直线
与
相交于
和
(
在
轴的上方,
在
轴的下方).
证明:
的斜率是定值;
求
、
、
、
、
所在直线的方程;
记
的面积为
,证明:数列
是等比数列,并求所有这些三角形的面积的和.
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/b1fdd5907c8945daa1d2a6c5f85cff33.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/e5bc5a88b190402ea0a5585796983893.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/480e1c5e5b41471fb3cbb691b8dd760c.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/254ded389dcb47029ef772c5050ecdb8.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/9d29b9adb3cd4d17863ebcba6f543736.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/e5bc5a88b190402ea0a5585796983893.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/900a3ffa563046c689438590dba753a8.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/a564e5d460ff45f084c9f06f50d168aa.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/25671a533b2f49da9491f03489380d64.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/422941d4ca564a3a9450487377c153fa.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/25671a533b2f49da9491f03489380d64.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/5c35b050df974373881b650ad5208d3f.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/422941d4ca564a3a9450487377c153fa.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/5c35b050df974373881b650ad5208d3f.png)
证明:
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/ee9191fbd491406bb810d9de498be548.png)
求
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/d5fd4eafdb57476fa2e30c7b9df32b1c.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/194610503a754b7686aa315734c59db2.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/ff5ec7535416488e8cc40f3416673c07.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/25671a533b2f49da9491f03489380d64.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/ff5ec7535416488e8cc40f3416673c07.png)
记
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/4899235549084d7b8c01254c4f1bc148.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/e506fc2c8bb4417f818d405cf4ed084b.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/c8fdf56ddd71474da71fa61f9cd63e63.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/f9a43993371a48cfa376a82c6752a9ed.png)
您最近一年使用:0次
3 . 一种作图工具如图1所示.
是滑槽
的中点,短杆
可绕
转动,长杆
通过
处铰链与
连接,
上的栓子
可沿滑槽AB滑动,且
,
.当栓子
在滑槽AB内做往复运动时,带动
绕
转动一周(
不动时,
也不动),
处的笔尖画出的曲线记为
.以
为原点,
所在的直线为
轴建立如图2所示的平面直角坐标系.
(Ⅰ)求曲线C的方程;
(Ⅱ)设动直线
与两定直线
和
分别交于
两点.若直线
总与曲线
有且只有一个公共点,试探究:
的面积是否存在最小值?若存在,求出该最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/505c6b1bb0214914813bd468e5658abd.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/f33972f039914ebfa9d824c29b1ce058.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/56a73279e3984bf789d920f038332a76.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/01dab6f0505b44b09fe64e1833a4a4ff.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/505c6b1bb0214914813bd468e5658abd.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/56a73279e3984bf789d920f038332a76.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/9927897ec3b34f83b734e2812f0050eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17df11e4f242f1ab2c664127a9cc4274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e47bb98258ebfcf1d8ad4bac10b7ba.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/9927897ec3b34f83b734e2812f0050eb.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/01dab6f0505b44b09fe64e1833a4a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/9927897ec3b34f83b734e2812f0050eb.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/01dab6f0505b44b09fe64e1833a4a4ff.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/3198a5c7ac1b44c19224417bc21c6725.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/9d5e5b28b9fc41f89792b5e3dfb97d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/13/7c593eff-1103-4bce-9ba1-1a807ac5c37d.png?resizew=337)
(Ⅰ)求曲线C的方程;
(Ⅱ)设动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b65826e98ba9bea060a68b4a66a2555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41bd9a29a1bde0ab8d008769bfd279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c42b4b5f59cf1e505febfb43f3f4647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046526976/STEM/680e72e7474b455bbfe34e88500a3a49.png)
您最近一年使用:0次
2016-12-03更新
|
4647次组卷
|
15卷引用:2015年全国普通高等学校招生统一考试理科数学(湖北卷)
2015年全国普通高等学校招生统一考试理科数学(湖北卷)2015年全国普通高等学校招生统一考试文科数学(湖北卷)(已下线)上海市华东师范大学第二附属中学2017-2018学年高三上学期10月月考数学试题北京市北京一零一中学2019-2020学年高二第一学期期末考试数学试题北京市101中学2019-2020学年上学期高二年级期末考试数学试题(已下线)专题29 圆锥曲线的综合问题-十年(2011-2020)高考真题数学分项安徽省马鞍山市第二中学2020-2021学年高二上学期期末理科数学试题(已下线)专题22 圆锥曲线的“三定”与探索性问题(讲)-2021年高三数学二轮复习讲练测(新高考版)(已下线) 专题26 圆锥曲线的“三定”与探索性问题(讲)-2021年高三数学二轮复习讲练测(文理通用)(已下线)专题23 圆锥曲线中的最值、范围问题 微点1 圆锥曲线中的最值问题贵州省遵义市南白中学2022-2023学年高二下学期第一次联考数学试题(已下线)专题24 解析几何解答题(文科)-4(已下线)专题24 解析几何解答题(理科)-3专题36平面解析几何解答题(第一部分)专题37平面解析几何解答题(第一部分)
20-21高二上·全国·课后作业
名校
4 . 对标准形式的抛物线,给出下列条件:
①焦点在y轴上;
②焦点在x轴上;
③抛物线上横坐标为1的点到焦点的距离等于6;
④由原点向过焦点的某直线作垂线,垂足坐标为(2,1).
其中满足抛物线方程为y2=10x的是____________ .(要求填写适合条件的序号)
①焦点在y轴上;
②焦点在x轴上;
③抛物线上横坐标为1的点到焦点的距离等于6;
④由原点向过焦点的某直线作垂线,垂足坐标为(2,1).
其中满足抛物线方程为y2=10x的是
您最近一年使用:0次
2021-04-18更新
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445次组卷
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5卷引用:3.3.1 抛物线及其标准方程(练习)
(已下线)3.3.1 抛物线及其标准方程(练习)(已下线)第七课时 课后 3.3.1 抛物线及其标准方程人教B版(2019) 选修第一册 过关检测 第二章 2.7.1 抛物线的标准方程(已下线)第14讲 抛物线的标准方程-【暑假自学课】2023年新高二数学暑假精品课(苏教版2019选择性必修第一册)安徽省合肥市第九中学2023-2024学年高二上学期第二次单元检测数学试题
名校
5 . 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
|
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
6 . 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
名校
7 . 已知椭圆
的左,右焦点分别为
,直线
与椭圆
交于
两点,给出下列结论:①若
,则
;②
与
不可能平行;③若
,则
;④
与
不可能垂直.其中正确结论的序号为__________ (请把正确结论的序号全部填写在横线上).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9835aacabfaabdf7e61da1d4e08b225a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73fbfd1b2f4b67ba5452bedcd1f5433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2015d9a88fb4d8f0520790693abc9649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80ecb6b5d5eca464b3f099513c08fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c429b542abf0ebee74a239b4857cf88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288060bacca802a86ff209ddfd412e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d76a73553016ef953653c8d92cd14d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
您最近一年使用:0次
解题方法
8 . 过抛物线
焦点
的直线与抛物线交于
两点,作
垂直抛物线的准线
于
,
为坐标原点,则下列结论正确的是_______ (填写序号).
①
;
②存在
,使得
成立;
③
;
④准线
上任意点
,都使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a8528cd0649f5a271a37f88ba532ba.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb35b2338cb644c9cc0000094ea63b23.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e902c3982957249ce719e9af7b98d292.png)
④准线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f387a4813c2ab2880cf66d768196c70.png)
您最近一年使用:0次
名校
解题方法
9 . 椭圆规是画椭圆的一种工具,如图1所示,在十字形滑槽上各有一个活动滑标
,
,有一根旋杆将两个滑标连成一体,
,
为旋杆上的一点,且在
,
两点之间,且
,当滑标
在滑槽
内做往复运动,滑标
在滑槽
内随之运动时,将笔尖放置于
处可画出椭圆,记该椭圆为
.如图2所示,设
与
交于点
,以
所在的直线为
轴,以
所在的直线为
轴,建立平面直角坐标系.
![](https://img.xkw.com/dksih/QBM/2020/8/13/2527164820111360/2530060390547456/STEM/8a2ee48e-5a90-4937-ac9e-b3684e18474a.png)
(1)求椭圆
的方程;
(2)设
,
是椭圆
的左、右顶点,点
为直线
上的动点,直线
,
分别交椭圆于
,
两点,求四边形
面积为
,求点
的坐标.
![](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/12ceb92b88602f8623ee9b034e1f4fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](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/23168940986f42abaffb417bb1f9df67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/2020/8/13/2527164820111360/2530060390547456/STEM/8a2ee48e-5a90-4937-ac9e-b3684e18474a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.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/39cc033406da2cdd342308972c6701f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291477a8e77c83c84a6b834b732f7f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-08-18更新
|
132次组卷
|
4卷引用:2020届云南省昆明市高三“三诊一模”教学质量检测数学(文)试题
2020届云南省昆明市高三“三诊一模”教学质量检测数学(文)试题(已下线)专题21 圆锥曲线综合-2020年高考数学(文)母题题源解密(全国Ⅲ专版)(已下线)专题20 圆锥曲线综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)山西省晋城市第一中学校2022-2023学年高二下学期第三次调研(5月)数学试题
名校
10 . 椭圆规是画椭圆的一种工具,如图1所示,在十字形滑槽上各有一个活动滑标
,
,
,有一根旋杆将两个滑标连成一体,
为旋杆上的一点,且在
,
两点之间,且
,当滑标
在滑槽
内做往复运动,滑标
在滑槽
内随之运动时,将笔尖放置于
处可画出椭圆,记该椭圆为
.如图2所示,设
与
交于点
,以
所在的直线为
轴,以
所在的直线为
轴,建立平面直角坐标系.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/f869f70b-4fff-43e5-a17c-6ec00ee048eb.png?resizew=372)
(1)求椭圆
的方程;
(2)设
是椭圆
上的两个不同点,若直线
、
的斜率之积为
(
为坐标原点),
是
的中点,连接
并延长椭圆
于点
,设
,求
的值.
![](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/ccb66bc3876219e9de0faafef8cb268d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](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/7b6ddc6dda8cbdfb288629996c09a4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/f869f70b-4fff-43e5-a17c-6ec00ee048eb.png?resizew=372)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c0b2b93ad71830f65aaf5a105bcda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次