To find the equation of the directrix of the given parabola [tex]\( y^2 = -24x \)[/tex], let's go through the necessary steps:
1. Identify the Form of the Parabola:
The given equation [tex]\( y^2 = -24x \)[/tex] is a standard form of a parabola opening to the left or right. It can be compared to the standard form [tex]\( y^2 = 4px \)[/tex].
2. Determine the Parameter [tex]\( p \)[/tex]:
By comparing [tex]\( y^2 = -24x \)[/tex] to [tex]\( y^2 = 4px \)[/tex], we can identify [tex]\( 4p = -24 \)[/tex].
3. Solve for [tex]\( p \)[/tex]:
[tex]\[
4p = -24 \implies p = \frac{-24}{4} = -6
\][/tex]
4. Find the Directrix:
For a parabola described by [tex]\( y^2 = 4px \)[/tex], the directrix is given by the equation [tex]\( x = -p \)[/tex].
[tex]\[
x = -(-6) = 6
\][/tex]
Therefore, the equation of the directrix of the given parabola is [tex]\( x = 6 \)[/tex].
The correct answer is:
D. [tex]\( x = 6 \)[/tex]
