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

**Solution:**

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

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

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

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|

By squaring both the 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

Hence, the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = -10 is x^{2} -12x - 20y = 64.

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

**Summary:**

The equation of the quadratic graph with a focus of (6, 0) and a directrix of y = -10 is x^{2} -12x - 20y = 64.

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