拋物線X^2=4Y的焦點(0,1)
即b=1
e=√2/2
c^2/a^2=1/2
a^2=b^2+c^2
a^2=2
右焦點F2
則BM⊥直線L,BM的斜率=-1
直線L的斜率=1
設橢圓右焦點為F,直線L的方程為
y=x+m與橢圓交于M(x1,y1),N(x2,y2)
3x²+4mx+2m²-2=0
x1+x2=-4m/3,x1x2=(2m²-2)/3
BN斜率 ×MF斜率(y2-1)y1/x2(x1-1)=-1
(y2-1)y1+x2(x1-1)=0
y1y2+x1x2-y1-x1=0
y1y2=(x1+m)(x2+m)=x1x2+m(x1+x2)+m²
x1x2+m(x1+x2)+m²-(x1+x2)-m+x1x2=0
2x1x2+m(x1+x2)--(x1+x2)-m+m²=0
2 ×(2m²-2)/3+m(-4m/3)+4m/3-m+m²=0
3m²+m-4=0
m=-4/3 m=1
直線L的方程為
y=x+1 y=x-4/3
打字好不容易呀