Question

Find the equation of the parabola whose vertex is at origin and focus is the point (0,-3) and what will be the equation of the directrix?

Answer 1

The equation of the parabola is x² = 12y

The equation of the directrix is y = -3

Given:

Vertex is Origin i.e. (0,0) and focus is the point (0,-3)

To Find:

The equation of the parabola

The equation of the directrix

Solution:

We have the focus formula as (0, a) = (0, -3).

Therefore, a = -3

The equation of the parabola is x² = - 4ay

Therefore, x² = - 4(-3)y

                  x² = 12y is the equation of parabola.                

We have the formula to find the equation of directrix as y = a

Therefore, y = -3 is the equation of the directrix.

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