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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]
D. [tex]x=6[/tex]


Sagot :

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]