...O,焦点在x轴上的椭圆E过点(0,1),离心率为根号2/2。 1.求椭圆E的...
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热心网友
其实不难，就是繁：
设出A点坐标，求出各点坐标表达式；
通过面积条件列方程，求出A点坐标值，再得出各点坐标值；
然后画出图形，有n种方法可求出内切圆。
热心网友
b = 1, c/a = sqrt(2)/2
c = sqrt(a^2 - b^2) = sqrt(a^2 - 1)
c^2/a^2 = 1-1/a^2 = 1/2
so a = sqrt(2), c=1
x^2/2 + y^2 = 1
2. equation of line L is y = k(x+1)
its intersecting points with E are obtained by solving
x^2 + 2k^2 (x+1)^2 - 2 = 0
x = (-2k^2 +/- sqrt(2k^2 - 2)/(2k^2 + 1)
you can get A,B's coordinate this way, and therefore C, and then M
area of MAF is a function of k
once k is obtained, M,A,F,C's coordinates are known
and you can get the equation of the circle
热心网友
焦点在x轴上的椭圆E过点(0,1),即b=1,离心率为根号2/2
即e=c/a=根号2/2,c^2/a^2=1/2
a^2=2c^2=2(a^2-b^2)=2(a^2-1), a^2=2
故椭圆E是:x^2/2+y^2=1.
左焦点坐标是(-1,0),设直线L的方程是y=k(x+1).设A(x1.y1),B(x2,y2),则有C(x1,-y1)
