# How do you identity if the equation #x^2-y^2+8x=16# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

The given equation fits the general Cartesian form of a conic section:

where

In the section entitled, Discriminant, the reference tells us to compute

The result is

To graph the hyperbola, I recommend that you write the equation in a form that gives you, the center, the vertices and the equations of the asymptotes:

center:

vertices:

asymptotes:

Let's work on that form.

Add

The expansion of the pattern

The absence of a y term tells us that

Substitute the left side of the pattern into the equation:

Substitute the values for h and k into the equation:

Simplify

Divide both sides by 32:

Write the denominators as squares:

The center is

The vertices

The equation of the asymptotes are:

Here is a graph with the equation, the center, the vertices and the asymptotes: