How to find the equation of a hyperbola when given the vertices and foci

Step-by-step explanation:

The vertices and foci are on the x-axis. Thus, the equation for the hyperbola will have the form x2a2-y2b2=1 x 2 a 2 - y 2 b 2 = 1. The vertices are (±6,0) (± 6, 0), so a=6 a = 6 and a2=36 a 2 = 36. The foci are (±2√10,0) (± 2 10, 0), so c=2√10 c = 2 10 and c2=40 c 2 = 40.