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

Jan 30, 2017

${x}^{2} = - 48 y$. 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 $\downarrow$. The

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

And so, the equation to the parabola is

${x}^{2} = - 4 a y = - 48 y$.

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