Question

A parabola has a vertex at the origin. The equation of the directrix of the parabola is y = 3. What are the coordinates of its focus?

Answer 1

focus -
(0,-3)

let me know if explanation needed.

Answer 2

Explanation:

Given that a parabola has a vertex at the origin.

The equation of the directrix of the parabola is y = 3.

When directrix is a horizontal line y =3 we find that distance of vertex from directrix is 3 units.

By definition of parabola, the focus lies on the axis of parabola which here is x=0(since perpendicular to y=3 and through vertex)

Since any point is equidistant from focus and directrix,

we get vertex is 3 units down from origin on y axis.

Hence focus is (0,-3)