# What is the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = −10?

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 (6, 0) and a directrix of y = −10 is x^{2} -12x - 20y = 64.

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

**Explanation:**

Given that, Focus = (6, 0) and directrix y = -10

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

Its distance from the focus point (6, 0) is √[(x − 6)^{2} + (y - 0)^{2}]

Its distance from directrix y = -10 is |y + 10|

Therefore, the equation will be:

√[(x − 6)^{2} + (y - 0)^{2}] = |y + 10|

Apply squaring on both sides.

(x − 6)^{2} + (y - 0)^{2} = (y + 10)^{2}

x^{2} -12x + 36 + y^{2} = y^{2} + 20y + 100

x^{2} -12x - 20y = 64