Aparabola can be drawn given a focus of(-5,−9) and a directrix of
y=−5. write the equation of the parabola in any form.

Step-by-step explanation:

Given:

Focus: (-5,-9)

Directrix: y = -5

Find: equation of the parabola

The equation of the line perpendicular to the directrix and passing through the focus is x = -5. This is the line of parabola's symmetry.

The distance between the focus and the directrix is the parabola's parameter, so

The vertex of the parabola lies on the line of symmetry and divides the distance between the focus and the directrix into two equal parts. So, its coordinates are (-5,-7).

Parabola goes in negative y-direction, thus, the equation of the parabola is