P(x1,y1) Q(x2,y2)
x1^2/a^2+y1^2/b^2=1
x2^2/a^2+y2^2/b^2=1 相减得
(x1-x2)(x1+x2)/a^2+(y1-y2)(y1+y2)/b^2=0
k=-1
直线L的方程 y=-x+1
2.向量OP=(x1,y1) 向量OQ=(x2,y2)
向量OP⊥向量OQ x1x2+y1y2=0
直线方程 y=-x+1 代入
x^2/a^2+y^2/b^2=1 b^2x^2+a^2y^2-a^2b^2=0
b^2(y^2+2y+1)+a^2y^2-a^2b^2=0
(b^2+a^2)y^2+2b^2y+(b^2-a^2b^2)=0
y1y2=(b^2-a^2b^2)/(b^2+a^2) y1+y2=-2b^2/(b^2+a^2)
x1x2=(y1y2)+(y1+y2)+1
x1x2+y1y2=2y1y2+(y1+y2)+1
=2(b^2-a^2b^2)/(b^2+a^2)-2b^2/(b^2+a^2)+1=0
.2a^2b^2=a^2+b^2
1/a^2+1/b^2=2
1／a2+1／b2为定值2