Question

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

A.) y = 1/12 x^2
B.) y = -1/12 x^2
C.) x = -1/12 y^2
D.) x = 1/12 y^12

Please explain how you got your answer.

Answer 1

x = -(1/12)y² is the real answer!!!!!

Answer 2

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 = -(1)/(12)x^(2)`