# 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 graph.

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|

By squaring both sides, we get,

(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

### Hence, 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.

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