# How do I graph the hyperbola represented by (x-2)^2/16-y^2/4=1?

Apr 22, 2017

Analyze the terms of the function given.

#### Explanation:

Since the y term of this equation is negative and the x term is positive, we know that this is a hourglass shaped graph and not a baseball shaped graph. The formula for a hyperbola is as follows:

$\frac{{\left(x - h\right)}^{2}}{a} ^ 2 - \frac{{\left(y - k\right)}^{2}}{b} ^ 2 = 1$

h is the distance the graph is shifted from the y-axis
k is the distance the graph is shifted from the x-axis.
a is the distance from the vertex of the graph to the center of the graph
b is used to indicate vertical stretch
A correlation between variables is ${a}^{2} + {b}^{2} = {c}^{2}$ where c is the distance from the foci of the graph to the center of the graph. Subsequently, c will always be greater than a.

graph{(((x-2)^2)/16)-((y^2)/4)=1 [-10, 10, -5, 5]}