Answered

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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]

Sagot :

GinnyAnsweridn
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]
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