Question

A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0).

What is the equation of the directrix of the parabola?

y = 3
y = –3
x = 3
x = –3

Answer 1

x= -3

Here's why: The directrix always goes behind the vertext of the parabola (thus the -3), and follows the curve (this parabola demands a vertical line, and we know x=a number creates a vertical line on a graph).

Answer 2

x= -3

Explanation:

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix .

The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola. If the axis of symmetry of a parabola is vertical, the directrix is a horizontal line .

focus of parabola=(3,0)

(y - k)² = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

Here, equation of parabola is:

y²=12x i.e. p=3,h=0

(since, focus is (3,0) i.e. k=0 and h+p=3 also at x=0 y=0 which will be true if h=0)

Hence, directrix is x= -3