过抛物线y^2=4x的焦点F作一直线交抛物线于P,Q两点,若线段PF与FQ的长分别是p、q,则1/p+1/q等于?

F(1,0)则是y-0=k(x-1)y=kx-k代入(kx-k)²=4xk²x²-(2k²+4)x+k²=0x1+x2=(2k²+4)/k²x1x2=1准线x=-1抛物线定义PF=P到准线距离所以p=x1+1.q=x2+11/p+1/q=1/(x1+1)+1/(x2+1)=(x1+x2+2)/...