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?
A) Y=3
B) Y= -3
C) X= 3
D) X= -3

Answer 1

Answer:

$\boxed{\boxed{x=-3}}$

Step-by-step explanation:

Relation between focus, vertex and directrix-

The vertex of the parabola is at equal distance between focus and the directrix. As any point on the parabola is equidistant from both focus and directrix.

And the directrix is always perpendicular to axis of symmetry and does not touch the parabola.

From the graph, the focus is at (3, 0) and axis of symmetry is x axis or y=0 line.

So the directrix will be horizontal and on the left of the parabola.

Hence, the equation of directrix of the given parabola will be x= -3

Answer 2

The correct answer is D X=-3, since the directrix is always the opposite distance from the vertex as the focus is.