How would i be able to do this problem, I can't figure it out.?

Question

Find an equation of the parabola with focus (0,-1/8) and directix y=1/8

Answer 1

Take a point(x,y)
Its distance to the focus squared is d= x^2 +(y+1/8)^2

Its distance to the directrix squared is (y-1/8)^2
By def. both should be equal

x^2 +y^2 +y/4 +1/64 = y^2 - y /4+1/64


x^2= -y/2 ===>y =-2x^2