题目
题型:不详难度:来源:
右准线l的方程为:x = 12。
(1)求椭圆的方程;(4分)
(2)在椭圆上任取三个不同点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202658-87130.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202658-55413.gif)
证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202658-92594.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202659-53977.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202659-33666.gif)
因焦点为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202659-87746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202659-38010.gif)
又右准线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-71064.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-47774.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-34475.gif)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-52620.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-90538.gif)
故所求椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-33997.gif)
(II)记椭圆的右顶点为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-48365.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-88816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-39260.gif)
假设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202702-75017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202702-43951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202702-18132.gif)
又设点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202703-23156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-71064.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202703-24058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202703-53539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202703-18702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-74102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-10487.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-92486.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-10487.gif)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-19921.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202705-79276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202705-56382.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202705-19022.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202659-33666.gif)
因焦点为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202659-87746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202659-38010.gif)
又右准线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-71064.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-47774.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-34475.gif)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-52620.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-90538.gif)
故所求椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-33997.gif)
(II)记椭圆的右顶点为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-48365.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-88816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202701-39260.gif)
假设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202702-75017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202702-43951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202702-18132.gif)
又设点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202703-23156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202700-71064.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202703-24058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202703-53539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202706-66406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-74102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-10487.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-92486.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-10487.gif)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202704-19921.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202705-79276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202705-56382.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202705-19022.gif)
核心考点
试题【(本小题满分12分)如图,中心在原点O的椭圆的右焦点为F(3,0),右准线l的方程为:x = 12。(1)求椭圆的方程;(4分)(2)在椭圆上任取三个不同点,使】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202243-48920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202243-89005.gif)
(1)求椭圆的离心率e
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202243-57734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202244-68891.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202244-58031.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202245-89701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202229-47702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202229-87767.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202229-96039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-43607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-90349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-33521.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-90349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202230-99579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202216-30497.gif)
(1)若椭圆C上的点A(1,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202216-10604.gif)
(2)设点P是(1)中所得椭圆上的动点,当P在何位置时,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202216-39926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202208-42247.gif)
(1)求椭圆的离心率;
(2)若平行四边形OCED的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202208-59944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202208-16881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202200-58333.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-94782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-30494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-50402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202201-17359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023202202-98253.gif)
最新试题
- 1甲同学将所学气体制取的知识整理如下,请你帮助他完成相关内容。(1)写出图中有标号仪器的名称:a _________、b_
- 2已知函数在上有最大值和最小值,求、的值。
- 3我国领土最东端、最北端所在的省区是:[ ]A.内蒙古 B.黑龙江省 C.辽宁省 D.黑龙江、内蒙古
- 4童星玩具厂工人的工作时间为:每月22天,每天8小时.工资待遇为:按件计酬,多劳多得,每月另加福利工资500元,按月结算.
- 52008年2月2日,李沧法院审理了一起团伙抢劫案。案犯是15个平均年龄不到20岁的年轻人,最小的仅15周岁,他们通过网络
- 6已知椭圆C:x2a2+y2b2=1(a>b>0)的离心率为33,右焦点F也是抛物线y2=4x的焦点.(1)求椭圆方程;(
- 7下列各组物质中,能互称为同分异构体的是( )A.CH3CH2CH3与B.蔗糖与麦芽糖C.淀粉与纤维素D.CH2=CHC
- 8重新排列下列语段,把它们组成一篇意思连贯的短文(第一段已给出) A. He walked towards th
- 9请给“日”字分别增加一个笔划,组成不同的四个汉字。______________________________
- 10有资料表明,目前全球变暖引发的异常高温,每年造成世界大城市中约6000人死亡。造成全球气候变暖的主要气体是:[
热门考点
- 1求未知数x: (1)8x3+27=0; (2)25(x﹣1)2=9.
- 2下列各句中,划线成语使用恰当的一句是:A.来西湖旅游的人们,面对水色山光,无不为大自然这巧夺天工的造化所折服。B.他本来
- 3下列标点符号使用有错误的一项是(2分) ( )A.“您看这布华丽不华丽?”那两位诚实的官员说,“陛下请看:多么
- 4We would probably all be amazed if we watched a videotape of
- 5Tom has the longest journey because he lives from
- 6已知定义在R上f(x)满足f(x+2)=f(x),且f(0)=8,则f(10)=( )A.10 B.-6C.8 D.
- 7[2009年福州市学业考试]血液中含水量最多并且与体内的物质运输有关的成分是( )A.红细胞B.白细胞C.血小板D.血
- 8读等高线图,完成下列问题 (1)图中数码①、②、③、④、⑤、⑦表示陡崖的是______,表示鞍部的是______.(2)
- 9国家最高科学技术奖设立于2000年,获奖者均在当代科学技术前沿取得了重大突破或者在科学技术发展中有卓越建树,在科技创新、
- 10读下图,回答题。 小题1:图中全部属于温带季风气候的岛屿或半岛是( )A.④B.③C.②D.①小题2:图中岛国的工业集