IDNLearn.com offers a unique blend of expert answers and community-driven insights. Our platform offers reliable and detailed answers, ensuring you have the information you need.

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]
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]