M(x,y)
y/(x+1)*y/(x-1)=-2
y^2=-2(x^2-1)
∴y^2/2+x^2=1
(2)
PQ斜率存在 【不存在时弦长为2√2】
设为k,PQ:y=kx+1
{y=kx+1
{y^2/2+x^2=1
==> (kx+1)²+2x²=2
==> (k²+2)x²+2kx-1=0
设P(x1,y1),Q(x2,y2)
则x1+x2=-2k/(k²+2),x1x2=-1/(k²+2)
|PQ|=√(k²+1)*√[(x1+x2)²-4x1x2]
=√(k²+1)*√[4k²/(k²+2)²+4/(k²+2)]
=2√(k²+1)*√[（2k²+2)/(k²+2)²]
=2√2*(k²+1)/(k²+2)
又|PQ|=3√2／2
∴2√2*(k²+1)/(k²+2)=3√2／2
4(k²+1)=3(k²+2)
k²=2
k=±√2