What is the equation of the parabola with a focus at (0,0) and a directrix of y= -3?

1 Answer
Apr 5, 2016

The equation of the parabola is #y=1/6*x^2-1.5#

Explanation:

Vertex is at mid point between focus#(0,0)#and directrix #(y=-3)#So vertex is at #(0,-1.5)# The equation of parabola is#y=a(x-0)^2-1.5=ax^2-1.5# Distance(d) of vertex from directrix is 1.5 and we know #d=1/(4|a|) or a = 1/(4*1.5)=1/6#Hence the equation of the parabola is #y=1/6*x^2-1.5# graph{1/6*x^2-1.5 [-10, 10, -5, 5]}