Question

what is the equation of the directrix of the parabola given by the equation $y^2 = -24x$?

a. $y = 4$

b. $x = 4$

c. $y = 6$

d. $x = 6$

Explanation:

Step1: Match to standard parabola form

The given parabola is $y^2 = -24x$, which matches the standard form $y^2 = -4px$ (opens left).

Step2: Solve for $p$

Set $4p = 24$, so $p = \frac{24}{4} = 6$.

Step3: Find directrix equation

For $y^2=-4px$, directrix is $x=p$. Substitute $p=6$: $x=6$.

Answer:

D. $x=6$