# What is the equation of the quadratic graph with a focus of (5, 6) and a directrix of y = 2?

We will use the concept of focal point and directrix to find the equation.

## Answer: The equation of the quadratic graph with a focus of (5, 6) and a directrix of y = 2 is x^{2} -10x - 8y - 57 = 0.

Let us see how we will use the concept of focal point and directrix to find the equation.

**Explanation:**

Given that, Focus = (5, 6) and directrix of y = 2

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

Its distance from the focus point (5, 6) is √[(x − 5)^{2} + (y - 6)^{2}]

Its distance from directrix y = 2 is |y - 2|

Therefore, the equation will be:

√[(x − 5)^{2} + (y - 6)^{2}]= |y - 2|

Apply squaring on both sides.

(x − 5)^{2} + (y - 6)^{2} = (y - 2)^{2}

x^{2} -10x + 25 + y^{2} - 12y + 36 = y^{2} - 4y + 4

x^{2} -10x - 8y - 57 = 0