What is the equation of a hyperbola with vertices (-5,0) and (5,0) and foci (-7,0) and (7,0) Please explain how to figure out whether it's a horizontal or vertical hyperbola?
The foci of the hyperbola has changing x-coordinates, hence it possesses a horizontal transverse axis.
By the midpoint formula, the center of the hyperbola occurs at the point (0, 0). Its foci are at (0+c, 0) and (0-c, 0). Hence c=(7-0)=7 and a=(5-0)=5
Therefore, the standard form of its equation is: