Question

If the focus of a parabola is $(0, -3)$ and its directrix is $y = 3$, then its equation is:

• A. $x^2 = 12y$
• B. $x^2 = -12y$
• C. $y^2 = 12x$
• D. $y^2 = -12x$
• E. $y^2 = x$

Hint:

For a parabola, the equation depends on the orientation and focal distance $a$, calculated from the focus and directrix.

Answer 1

The Correct Option is B

The vertex of the parabola is the midpoint of the focus and directrix: $$\left( 0, \frac{-3 + 3}{2} \right) = (0,0)$$ The standard form of a parabola with its vertex at $(0,0)$ and vertical axis is: $$x^2 = 4ay$$ The focal distance is: $$a = -3$$ Thus, $$x^2 = -12y$$