Answer
$$\eqalign{
& {\text{Vertices }}\left( {0, - 4} \right){\text{ and }}\left( {0,4} \right) \cr
& {\text{Foci }}\left( {0, - 5} \right){\text{ and }}\left( {0,5} \right) \cr
& {\text{Asymptotes: }}y = \frac{4}{3}x{\text{ and }}y = - \frac{4}{3}x \cr} $$
Work Step by Step
$$\eqalign{
& \frac{{{y^2}}}{{16}} - \frac{{{x^2}}}{9} = 1 \cr
& {\text{The equation is in the standard form }}\frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}} = 1.{\text{ Then,}} \cr
& \frac{{{y^2}}}{{16}} - \frac{{{x^2}}}{9} = 1,\,\,\,\,\,a = 4,\,\,\,b = 3 \cr
& c = \sqrt {{a^2} + {b^2}} = \sqrt {{4^2} + {3^2}} = 5 \cr
& \cr
& {\text{With:}} \cr
& {\text{Vertices }}\left( {0, - a} \right){\text{ and }}\left( {0,a} \right) \cr
& {\text{Vertices }}\left( {0, - 4} \right){\text{ and }}\left( {0,4} \right) \cr
& {\text{Foci }}\left( {0, - c} \right){\text{ and }}\left( {0,c} \right) \cr
& {\text{Foci }}\left( {0, - 5} \right){\text{ and }}\left( {0,5} \right) \cr
& {\text{Asymptotes: }}y = \frac{a}{b}x{\text{ and }}y = - \frac{a}{b}x \cr
& {\text{Asymptotes: }}y = \frac{4}{3}x{\text{ and }}y = - \frac{4}{3}x \cr
& \cr
& {\text{Graph}} \cr} $$
