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kOM=y0/x0=(y1+y2)/(x1+x2)=k1
kPQ=(y1-y2)/(x1-x2)
设PQ的方程y=kx+m
x²/a²+(kx+m)²/b²=1
b²x²+a²(k²x²+2kmx+m²)=a²b²
(b²+a²k²)x²+2a²kmx+(a²m²-a²b²)=0
x1+x2=-2a²km/(b²+a²k²)
y1+y2=k(x1+x2)+2m=-2a²k²m/(b²+a²k²)+2m=(-2a²k²m+2mb²+2a²k²m)/(b²+a²k²)=2mb²/(b²+a²k²)
k1k=k.2mb²/(-2a²km)=-b²/a²
kPQ=(y1-y2)/(x1-x2)
设PQ的方程y=kx+m
x²/a²+(kx+m)²/b²=1
b²x²+a²(k²x²+2kmx+m²)=a²b²
(b²+a²k²)x²+2a²kmx+(a²m²-a²b²)=0
x1+x2=-2a²km/(b²+a²k²)
y1+y2=k(x1+x2)+2m=-2a²k²m/(b²+a²k²)+2m=(-2a²k²m+2mb²+2a²k²m)/(b²+a²k²)=2mb²/(b²+a²k²)
k1k=k.2mb²/(-2a²km)=-b²/a²
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追答
ΔOPQ=(1/2)|x1y2-x2y1|
= (1/2)|x1(kx2十m)-x2(kx1十m)|
= (1/2)|m(x1-x2)|
=√2
m²(x1-x2)²=8
m²[(x1十x2)²-4x1x2]=8
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