The Hyperbola Question?

Question

Graph (x^2 / a^2) – (y^2 / b^2) = 1 and (x^2 / a^2) – (y^2 / b^2) = -1 in the same viewing rectangle for values of a^2 and b^2 of your choice. Describe the relationship between the two graphs.

Answer 1

Changing the sign of the 1 reverses the roles of x and y.
The first case is an east-west opening hyperbola with the x axis as the major axis, the second case is a north-south opening hyperbola with the y axis as the major axis. Both are centered at the origin.