Question

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

Answer 1

Answer:

$y = - \frac{1}{12} {x}^{2}$

Step-by-step 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:

${x}^{2} = - 4 \times 3y$

${x}^{2} = -12y$

Hence the equation is

$y = - \frac{1}{12} {x}^{2}$