# Prove that the locus is a parabola

The point P(x,y) moves in XY plane such as that its distance from a fixed point (0,-1) is equal to its distance from the line Y=1. Prove that the locus is a parabola. Find it's focus, directrix, vertex, axis of symmetry and focal length.

I really need help and don't have much of an idea of how to do this.

• Man its high school mathematics... – Troy Woo Aug 17 '14 at 8:36

Since we have $$(x-0)^2+\{y-(-1)\}^2=|y-1|^2,$$ we have $$x^2=4\cdot (-1)\cdot y.$$ The vertex is $(0,0)$, the axis of symmetry is $x=0$, the focus is $(0,-1)$, the directrix is $y=-(-1)$.