A parabola can be represented by the equation [tex]y^2 = 12x[/tex].

Which equation represents the directrix?

A. [tex]y = -3[/tex]
B. [tex]y = 3[/tex]
C. [tex]x = -3[/tex]
D. [tex]x = 3[/tex]



Answer :

To determine the equation that represents the directrix of the given parabola, we need to start by analyzing the standard form of the parabola.

The given equation of the parabola is:

[tex]\[ y^2 = 12x \][/tex]

1. Identify the standard form:

The standard form for a parabola that opens to the right is:

[tex]\[ y^2 = 4px \][/tex]

where [tex]\( p \)[/tex] is the distance from the vertex to the focus (or from the vertex to the directrix, but in the opposite direction).

2. Compare to find [tex]\( p \)[/tex]:

By comparing the given equation [tex]\( y^2 = 12x \)[/tex] with the standard form [tex]\( y^2 = 4px \)[/tex], we can identify the value of [tex]\( p \)[/tex]:

[tex]\[ 4p = 12 \][/tex]

Solving for [tex]\( p \)[/tex]:

[tex]\[ p = \frac{12}{4} \][/tex]
[tex]\[ p = 3 \][/tex]

3. Determine the directrix:

The directrix of a parabola given in the form [tex]\( y^2 = 4px \)[/tex] is a vertical line located at [tex]\( x = -p \)[/tex].

Since [tex]\( p = 3 \)[/tex]:

[tex]\[ x = -3 \][/tex]

Therefore, the equation that represents the directrix of the given parabola [tex]\( y^2 = 12x \)[/tex] is:

[tex]\[ x = -3 \][/tex]

So the correct answer is:

[tex]\[ x = -3 \][/tex]