What is the equation of a hyperbola with a = 9 and c = 12? Assume that the transverse axis is horizontal

Given a and c, we solve for b by using the formula:

c² = a² + b²

12² = 9² + b²

b = 3√7

The standard equation for a hyperbola with a horizontal transverse axis is

(x-h) ²/a² - (y-k) ²/b² = 1, where (h, k) is the center.

Assuming that center is (0,0), the equation of the hyperbola will be:

x²/9² - y² / (3√7) ² = 1 or

x²/81 - y²/63 = 1