# Derive the Equation of the Parabola with a Focus at (0, -4) and a Directrix of y = 4.

We will be solving this by using the focus point and the directrix.

## Answer: The Equation of the Parabola with a Focus at (0, -4) and a Directrix of y = 4 is x^{2} + 16y = 0.

Let us solve this step by step.

**Explanation:**

Given that, Focus = (0, -4) and directrix y = 4

Let us suppose that there is a point (x, y) on the parabola.

Its distance from the focus point (0, -4) is √(x − 0)^{2} + (y + 4)^{2}

Its distance from directrix y = 4 is |y - 4|

Therefore, the equation will be:

√(x − 0)^{2} + (y + 4)^{2} = |y - 4|

Apply square on both sides.

(x − 0)^{2} + (y + 4)^{2} = (y - 4)^{2}

x^{2} + y^{2} + 8y + 16 = y^{2} - 8y + 16

x^{2} + 16y = 0