Question

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

Answer 1

Focus has coordinates (0, a)
a = -3
Thus, 4a = 4(-3) = -12

Because a is negative, we know it will be a concave down or concave left parabola. Hence, A and D can be eliminated. And we know it has to be B because the directrix is the horizontal line y = 3. Hence, the equation of the parabola becomes:

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