# Derive the Equation of the Parabola with a Focus at (-5, 5) and a Directrix of y = -1.

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

## Answer: The Equation of the Parabola with a Focus at (-5, 5) and a Directrix of y = -1 is x^{2} + 10x - 12y + 49 = 0.

Let us solve this step by step.

**Explanation:**

Given that, Focus = (-5, 5) and directrix y = -1

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

Its distance from the focus point (-5, 5) is √(x + 5)^{2} + (y - 5)^{2}

Its distance from directrix y = -1 is |y + 1|

Therefore, the equation will be:

√(x + 5)^{2} + (y - 5)^{2} = |y + 1|

Apply square on both sides.

(x + 5)^{2} + (y - 5)^{2} = (y + 1)^{2}

x^{2} + 10x + 25 + y^{2} - 10y + 25 = y^{2} + 2y + 1

x^{2} + 10x - 12y + 49 = 0