题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-29943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-44640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-49112.png)
(1)求双曲线的离心率.
(2)过双曲线E的右焦点且斜率为1的直线交双曲线于A,B两点,O为坐标原点,C为双曲线上一点,满足
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-14184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-39648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-36455.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-58584.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-49112.png)
(2)联立方程,设出A,B,
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-14184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-14184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-39648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-36455.png)
解:(1)由点P(x0,y0)(x0≠±a)在双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-29943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-44640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-13281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024922-30758.png)
由题意又有
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024922-80476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024922-83767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-49112.png)
可得a2=5b2,c2=a2+b2=6b2,则e=
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024922-51911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-58584.png)
(2)联立方程得
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024923-70764.png)
得4x2-10cx+35b2=0,
设A(x1,y1),B(x2,y2),
则
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024923-37744.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-14184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024920-14184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-39648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024921-36455.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024923-87502.png)
又C为双曲线E上一点,即
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024923-52804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024924-11325.png)
有(λx1+x2)2-5(λy1+y2)2=5b2,
化简得:λ2(
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024924-62886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024924-31041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024924-53225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024925-85079.png)
又A(x1,y1),B(x2,y2)在双曲线E上,
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024924-62886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024924-31041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024924-53225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024925-85079.png)
又x1x2-5y1y2=x1x2-5(x1-c)(x2-c)
=-4x1x2+5c(x1+x2)-5c2=10b2,
得:λ2+4λ=0,解出λ=0或λ=-4.
核心考点
试题【P(x0,y0)(x0≠±a)是双曲线E:-=1(a>0,b>0)上一点,M,N分别是双曲线E的左,右顶点,直线PM,PN的斜率之积为.(1)求双曲】;主要考察你对双曲线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/20191024/20191024024914-98648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024914-72203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024914-22513.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024908-88940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024908-82853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024908-79149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024902-79518.png)
A.6![]() | B.4 | C.2 | D.1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024857-80056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024858-31703.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024024852-88840.jpg)
最新试题
- 1“我和你心连心,同住‘地球村’……”,下列能够突出反映“地球村”这一当今世界特征的是①美国波音公司在全世界范围内组织零件
- 2下列变化中,属于化学变化的是 A.汽油挥发B.冰雪融化C.铜丝弯曲D.燃放烟火
- 3患坏血病是因为人体中缺乏A.维生素AB.维生素BC.维生素CD.维生素D
- 4【题文】“2010年高考作文错一字扣1分。”教育部考试中心出台的新规定引起了考生和家长的极大关注,请你根据提供的情景各写
- 5元朝时期,中央政府对辽阔的地域实行有效控制和管理的措施是( )A.实行行省制度B.实行册封制度C.实行三省六部制
- 6新文化运动时期,陈独秀认为真正可以“救治中国政治上、道德上、学术上、思想上一切黑暗的是” [ ]A.共产主义
- 7菱形的两条对角线的长分别是5cm和4cm,面积为______cm2.
- 8下列各物质的溶液既能跟某些酸反应又能跟某些碱溶液反应的是( )A.KNO3B.MgCl2C.NaOHD.K2CO3
- 9家鸽适于飞行生活的形态结构和生理特点主要表现在以下几个方面(1)家鸽的身体呈 型,可以减少空气阻力,
- 10是,,,的平均数,是,,,的平均数,是,,,的平均数,则下列各式正确的是( )A.B.C.D.
热门考点
- 1敦煌莫高窟被称为世界最大的艺术宝库之一,主要是因为A.石窟中唐代的艺术品居多B.窟内有大量的碑刻书法C.窟内有大量精美的
- 2This is my school ________ is near the post office.
- 3【题文】北京时间2008年8月8日20时整,第29届奥运会开幕式在北京鸟巢体育馆举行,位于纽约(西五区)的华侨收看直播节
- 4下列各项中,标点符号使用合乎规范的一项是( )A.经国务院授权,国务院新闻办公室今天发布“国家人权行动计划(2009-
- 5Nowadays, there is a ________ increase in children"s creativ
- 6 在图中,EF、GH为平行的金属导轨,其电阻不计,R为电阻,C为电容器,AB为可在EF和GH上滑动的导体横杆.有匀强磁场
- 7函数f(x)=logax(a>0,a≠1),若f(x1x2…x2009)=16,则f(x12)+f(x22)+…+f(x
- 8质量为M的人站在地面上,用绳通过定滑轮将质量为m的重物从高处放下,如右图所示,若重物以加速度a向下降落(a<g),
- 9There are three libraries in our school, ______ were built f
- 10 设平面向量a="(x1,y1),b=(x2,y2)" ,定义运算⊙:a⊙b ="x1y2-y1x2" .已知平面向量a