Question

The equation of the parabola whose focus is $(6, 0)$ and directrix is $x = -6$ is:

• A. $y^2 = 24x$
• B. $y^2 = -24x$
• C. $x^2 = 24y$
• D. $x^2 = -24y$

Answer 1

The Correct Option is A

The focus is $(6, 0)$, and the directrix is $x = -6$.

The vertex is midway between the focus and directrix: Vertex = $\left(\frac{6 + (-6)}{2}, 0\right) = (0, 0)$. 

The parabola opens to the right. 

The equation of the parabola is: $y^2 = 4ax$, where $a = 6$. 

Substituting $a = 6$, we get: $y^2 = 24x$.