# What is the equation of a hyperbola with a=6 and c=9?

${c}^{2} = {a}^{2} + {b}^{2}$ $\implies$ ${9}^{2} = {6}^{2} + {b}^{2}$ $\implies$ ${b}^{2} = 81 - 36$ $\implies$ ${b}^{2} = 45$ $\implies$ $b = \pm 3 \sqrt{5}$
${x}^{2} / {a}^{2} - {y}^{2} / {b}^{2} = 1$ $\implies$ ${x}^{2} / 36 - {y}^{2} / 45 = 1$, that is the equation of the hyperbola.