已知椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809017_ST/0.png)
的一个顶点到其左、右两个焦点F
1,F
2的距离分别为5和1;点P是椭圆上一点,且在x轴上方,直线PF
2的斜率为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809017_ST/1.png)
.
(Ⅰ)求椭圆E的方程;
(Ⅱ)求△F
1PF
2的面积.
考点分析:
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(Ⅰ)求以点F
1(-2,0),F
2(2,0)分别为左右焦点,且经过点P(3,-2
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809016_ST/0.png)
)的椭圆的标准方程;
(Ⅱ)求中心在原点,焦点在坐标轴上,离心率为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809016_ST/1.png)
,且经过点P(4,-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809016_ST/2.png)
)的双曲线的方程.
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2+2(m-2)x-3m+10=0无实数根.若p∨q为真,p∧q为假,求实数m的取值范围.
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如图,双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809014_ST/0.png)
-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809014_ST/1.png)
=1(a,b>0)的两顶点为A
1,A
2,虚轴两端点为B
1,B
2,两焦点为F
1,F
2.若以A
1A
2为直径的圆内切于菱形F
1B
1F
2B
2,切点分别为A,B,C,D.则:
(Ⅰ)双曲线的离心率e=
;
(Ⅱ)菱形F
1B
1F
2B
2的面积S
1与矩形ABCD的面积S
2的比值
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809014_ST/2.png)
=
.
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已知双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809013_ST/0.png)
-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102739135980969/SYS201311031027391359809013_ST/1.png)
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1、F
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.
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2=2px (p>0)上一点P(6,m)到其焦点F的距离为7,则抛物线C的以点M(2,1)为中点的弦AB所在直线的方程为
.
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