Question

过抛物线y^2=2px p>0的焦点F作一直线相交于A,B,AF=M.FB=N 则1/M+1/N=?

Answer 1

设A（x1,y1）,B（x2,y2）

1/M+1/N=1/(p/2 +x1)+1/(p/2 +x2)

=(p+x1+x2)/(p^2/4 +p/2(x1+x2)+x1x2)

=(p+x1+x2)/p^2/2 +p/2(x1+x2)

=(p+x1+x2)/（p/2(p+x1+x2))

=2/p