焦點(diǎn)在Y軸,設(shè)橢圓方程為：y^2/b^2+x^2/a^2=1,(b>a>0),直線y=3x-2與橢圓相交于A（x1,y1),B(x2,y2)兩點(diǎn),
b^2-a^2=c^2=50,
a^2=b^2-50,
y^2/b^2+x^2/(b^2-50)=1,
y1^2/b^2+x1^2/(b^2-50)=1,(1)
y2^2/b^2+x2^2/(b^2-50)=1,(2)
(1)-(2)式,
(y1^2-y2^2)/b^2+(x1^2-x^2)/(b^2-50)=0,
[(y1-y2)/(x1-x2)]*[(y1+y2)/2/(x1+x2)/2]+b^/(b^2-50)=0,(3)
(y1-y2)/(x1-x2)=k=3,
設(shè)中點(diǎn)坐標(biāo)為M（x0,y0),x0=(x1+x2)/2=1/2,
y0=3x0-2=-1/2,y0=(y1+y2)/2,
代入（3）式,
3*(-1/2)/(1/2)+b^2/(b^2-50)=0,
b^2=75,
a^2=b^2-50=25,
∴橢圓的方程為：y^2/75+x^2/25=1.