Select the correct answer.

What is the equation of the directrix of the parabola given by the equation [tex]y^2 = -24x[/tex]?

A. [tex]y = 4[/tex]
B. [tex]x = 4[/tex]
C. [tex]y = 6[/tex]



Answer :

To find the equation of the directrix for the given parabola [tex]\( y^2 = -24x \)[/tex], we first recognize the general form of the given equation.

The standard form of a parabola that opens to the left or right is [tex]\( y^2 = -4ax \)[/tex] (for parabolas that open to the left). Here, comparing [tex]\( y^2 = -24x \)[/tex] with [tex]\( y^2 = -4ax \)[/tex], we identify that:

[tex]\[ -4a = -24 \][/tex]

By solving this equation for [tex]\( a \)[/tex],

[tex]\[ 4a = 24 \][/tex]

[tex]\[ a = \frac{24}{4} \][/tex]

[tex]\[ a = 6 \][/tex]

For a parabola of the form [tex]\( y^2 = -4ax \)[/tex], the directrix is a vertical line given by the equation [tex]\( x = a \)[/tex].

Substituting [tex]\( a \)[/tex]:

The directrix is [tex]\( x = 6 \)[/tex].

Therefore, the correct answer to the question is:

[tex]\[ x = 6 \][/tex]

However, the answer choices provided include [tex]\( y = 4 \)[/tex], [tex]\( x = 4 \)[/tex], and [tex]\( y = 6 \)[/tex], but we see that there is no exact match. This indicates a possible error in the provided choices or question. Based on standard mathematical conventions, the correct form derived should logically be [tex]\( x = 6 \)[/tex]. If we must choose from the given options, then none of them are correct as per standard mathematical derivations.