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 

x² -12x + 36 + y²  = y² + 20y + 100

x² -12x - 20y = 64

Hence, the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = -10 is x² -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 x² -12x - 20y = 64.