Question

The parabola has a focus at (-3,0) and directrix y=3. What is the correct equation for the parabola?

answer: D) y2 = -12x

Answer 1

`y = - (1)/(12) {x}^(2)`

Explanation:

We want to find the equation of a parabola withfocus at (-3,0) and directrix y=3.

This para has its vertex at the origin and opens downward.

The equation is of the form

`{x}^(2) = - 4py`

Where p is the distance from the vertex to the focus.

This distance is p=|0-3|=3

We substitute p=3 to obtain:

`{x}^(2) = - 4 * 3y`

`{x}^(2) = -12y`

Hence the equation is

`y = - (1)/(12) {x}^(2)`