Answer
$$\frac{{{x^2}}}{{36}} - \frac{{{y^2}}}{{64}} = 1$$
Work Step by Step
$$\eqalign{
& {\text{Center }}\left( {0,0} \right) \cr
& {\text{Vertex }}\left( {6,0} \right) \cr
& {\text{Focus }}\left( {10,0} \right) \cr
& {\text{The hyperbola has the standard form,}} \cr
& \frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1 \cr
& {\text{With: }} \cr
& {\text{Vertices }}\left( { - a,0} \right){\text{ and }}\left( {a,0} \right) \cr
& {\text{Vertex }}\left( {6,0} \right) \to a = 6 \cr
& {\text{Foci }}\left( { - c,0} \right){\text{ and }}\left( {c,0} \right) \cr
& {\text{Focus }}\left( {10,0} \right) \to c = 10 \cr
& {b^2} = {c^2} - {a^2} = 100 - 36 = 64 \cr
& \underbrace {\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1}_ \downarrow \cr
& \frac{{{x^2}}}{{36}} - \frac{{{y^2}}}{{64}} = 1 \cr} $$
