椭圆ax2+by2=1与直线x+y-1=0相交于A、B两点,C是AB的中点,|AB|=2√2,O为坐标原点,OC的斜率为（√2）/2
OC:y=(√2/2)x
AB:x+y-1=0
x+(√2/2)x-1=0
xC=2/(2+√2),yC=√2/(2+√2)
C[2/(2+√2),√2/(2+√2)]
xA+xB=2xC=4/(2+√2),yA+yB=2yC=2√2/(2+√2)
x+y-1=0
y=1-x
ax^2+by^2=1
ax^2+b(1-x)^2=1
(a+b)x^2-2bx+b-1=0
xA+xB=2b/(a+b)=4/(2+√2),b=(√2)a
xA*xB=(b-1)/(a+b)=(√2a-1)/(a+√2a)
(xA+xB)^2=8/(3+2√2)
(xA-xB)^2=(yA-yBV)^2=(xA+xB)^2-4xA*xB=8/(3+2√2)-4(√2a-1)/(a+√2a)
(xA-xB)^2+(yA-yB)^2=AB^2
2[8/(3+2√2)-4(√2a-1)/(a+√2a)]=(2√2)^2=8
2/(3+2√2)-(√2a-1)/(a+√2a)=1
2/(3+2√2)-1=(√2a-1)/(a+√2a)
(-1-2√2)/(3+2√2)=(√2a-1)/(a+√2a)
a=1/3
b=(√2)a=√2/3