Question

question 20 of 30
what is the equation of the directrix of the parabola defined by the equation shown below?
$x^{2}=24y$
a. $y = - 6$
b. $x = - 9$
c. $y = 9$
d. $x = 4$

Explanation:

Step1: Recall the standard - form of parabola

The standard form of a parabola opening upwards or downwards is $x^{2}=4py$. Comparing $x^{2}=24y$ with $x^{2}=4py$, we have $4p = 24$.

Step2: Solve for $p$

Dividing both sides of the equation $4p = 24$ by 4, we get $p=\frac{24}{4}=6$.

Step3: Find the directrix

For a parabola of the form $x^{2}=4py$ opening upwards, the equation of the directrix is $y=-p$. Since $p = 6$, the equation of the directrix is $y=-6$.

Answer:

A. $y = - 6$