Question

A parabola can be represented by the equation y2 = 12x. which equation represents the directrix?

Answer 1

The equation of the directrix is x = -3

What is Parabola?

A mirror-symmetrical, roughly U-shaped plane curve known as a parabola. It corresponds to a number of mathematical models that appear to be superficially dissimilar but yet all define the exact same curves. A point and a line are one way to describe a parabola.

According to the given information:

Given the general equation of a parabola expressed as

(y-y0)² = 4a(x-x0) ... 1

Equation of the directrix will be expressed as x = x0 - a

From the equation given;

y² = 12x ... 2

Comparing 1 and 2;

x - x0 = x

-x0 = x - x

-x0 = 0

x0 = 0

Similarly;

y-y0 = y

-y0 = y - y

-y0 = 0

y0 = 0

Also;

4a = 12

a = 12/4

a = 3

Substituting x0 =0, y0 = 0 and a = 3 into the equation of the directrix above, we will have;

x = x0 - a

x = 0 - 3

x = -3

Hence,

the equation of the directrix is x = -3

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