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

Solution:

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

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 

x² - 10x + 25 + y² - 12y + 36 = y² - 4y + 4

x² - 10x - 8y + 57 = 0

Hence, the equation of the quadratic graph with a focus of (5, 6) and a directrix of y = 2 is x² - 10x - 8y + 57 = 0.

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

Summary:

The equation of the quadratic graph with a focus of (5, 6) and a directrix of y = 2 is x² -10x - 8y + 57 = 0.