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

GinnyAnswer
To determine the equation of the directrix of the parabola represented by [tex]\( y^2 = 12x \)[/tex], let's follow these steps:

1. Identify the form of the parabola:
The standard form of a parabola that opens either to the right or left is [tex]\( y^2 = 4ax \)[/tex], where [tex]\( a \)[/tex] is a constant.

2. Match the given equation to the standard form:
Compare the given equation [tex]\( y^2 = 12x \)[/tex] to [tex]\( y^2 = 4ax \)[/tex] to find the value of [tex]\( a \)[/tex].

- Here, [tex]\( 4a = 12 \)[/tex].

3. Solve for [tex]\( a \)[/tex]:
To find [tex]\( a \)[/tex], divide both sides of the equation [tex]\( 4a = 12 \)[/tex] by 4:

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

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

5. Substitute the value of [tex]\( a \)[/tex]:
Substitute [tex]\( a = 3 \)[/tex] into the directrix equation:

[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]\[ \boxed{x = -3} \][/tex]
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