Question

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

Answer 1

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:

`((x-h)^2)/a^2-((y-k)^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]}