Question

What is the equation of a parabola with vertex (0, 0) and directrix y = 12?

Answer 1

`x^2=-48y`. See graph.

Explanation:

Tangent at the vertex V(0, 0) is parallel to directrix y = 12, and so, its

equation is y = 0 and the axis of the parabola is y-axis `darr`. The

size of the parabola a = distance of V from the directrix = 12.

And so, the equation to the parabola is

`x^2=-4ay=-48y`.

graph{(x^2+48y)y(y-12)x=0 [-40, 40, -20, 20]}