Answer
$$\eqalign{
& {\text{Vertices }}\left( {0, - 2} \right){\text{ and }}\left( {0,2} \right) \cr
& {\text{Foci }}\left( {0, - \sqrt {29} } \right){\text{ and }}\left( {0,\sqrt {29} } \right) \cr
& {\text{Asymptotes: }}y = \frac{2}{5}x{\text{ and }}y = - \frac{2}{5}x \cr} $$
Work Step by Step
$$\eqalign{
& 25{y^2} - 4{x^2} = 100 \cr
& {\text{Divide the equation by 100}} \cr
& \frac{{{y^2}}}{4} - \frac{{{x^2}}}{{25}} = 1 \cr
& {\text{The equation is in the standard form }}\frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}} = 1.{\text{ Then,}} \cr
& \frac{{{y^2}}}{4} - \frac{{{x^2}}}{{25}} = 1,\,\,\,\,\,a = 2,\,\,\,b = 5 \cr
& c = \sqrt {{a^2} + {b^2}} = \sqrt {4 + 25} = \sqrt {29} \cr
& \cr
& {\text{With:}} \cr
& {\text{Vertices }}\left( {0, - a} \right){\text{ and }}\left( {0,a} \right) \cr
& {\text{Vertices }}\left( {0, - 2} \right){\text{ and }}\left( {0,2} \right) \cr
& {\text{Foci }}\left( {0, - c} \right){\text{ and }}\left( {0,c} \right) \cr
& {\text{Foci }}\left( {0, - \sqrt {29} } \right){\text{ and }}\left( {0,\sqrt {29} } \right) \cr
& {\text{Asymptotes: }}y = \frac{a}{b}x{\text{ and }}y = - \frac{a}{b}x \cr
& {\text{Asymptotes: }}y = \frac{2}{5}x{\text{ and }}y = - \frac{2}{5}x \cr
& \cr
& {\text{Graph}} \cr} $$
