Question

抛物线x2＝y上一点A的纵坐标为4,则点A与抛物线焦点的距离为?

Answer 1

x^2=y

纵坐标y=4时,x^2=4,x=±2,A（±2,4）

x^2=y=2*1/2*y,焦点纵坐标1/2÷2=1/4, 即焦点（0,1/4)

点A与抛物线焦点的距离 = √{(xA-0)^2+(yA-1/4)^2} = √{2^2+(4-1/4)^2} = 17/4