(1/2)椭圆ax^2+bx^2=1与直线x+y－1＝0相交于A,B两点,C是AB的中点,若|AB|=2倍根号2,OC的斜率为根号2/...(1/2)椭圆ax^2+bx^2=1与直线x+y－1＝0相交于A,B两点,C是AB的中点,若|AB|=2倍根号2,OC的斜率为根号2/2,求椭

Question

(1/2)椭圆ax^2+bx^2=1与直线x+y－1＝0相交于A,B两点,C是AB的中点,若|AB|=2倍根号2,OC的斜率为根号2/...
(1/2)椭圆ax^2+bx^2=1与直线x+y－1＝0相交于A,B两点,C是AB的中点,若|AB|=2倍根号2,OC的斜率为根号2/2,求椭圆

Answer 1

A（x1,y1）B（x2,y2）
a(x1-x2)(x1+x2)+b(y1-y2)(y1+y2)=0,(y1-y2)/(x1-x2)= -1
(y1+y2)/(x1+x2)=√2/2,a√2=b
|AB|=2√2=√[(x1+x2)^2-4x1x2]√2
a=(2+√2)/2,b=1+√2
方程[(2+√2)/2]x^2+(1+√2)y^2=1