Answer
$$\eqalign{
& {\text{Vertices }}\left( { - \sqrt {14} ,0} \right){\text{ and }}\left( {\sqrt {14} ,0} \right) \cr
& {\text{Foci }}\left( { - \sqrt {34} ,0} \right){\text{ and }}\left( {\sqrt {34} ,0} \right) \cr
& {\text{Asymptotes: }}y = \frac{{2\sqrt 5 }}{{\sqrt {14} }}x{\text{ and }}y = - \frac{{2\sqrt 5 }}{{\sqrt {14} }}x \cr} $$
Work Step by Step
$$\eqalign{
& 10{x^2} - 7{y^2} = 140 \cr
& {\text{Divide the equation by 140}} \cr
& \frac{{{x^2}}}{{14}} - \frac{{{y^2}}}{{20}} = 1 \cr
& {\text{The equation is in the standard form }}\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1.{\text{ Then,}} \cr
& \frac{{{x^2}}}{{14}} - \frac{{{y^2}}}{{20}} = 1,\,\,\,\,\,a = \sqrt {14} ,\,\,\,b = 2\sqrt 5 \cr
& c = \sqrt {{a^2} + {b^2}} = \sqrt {14 + 20} = \sqrt {34} \cr
& \cr
& {\text{With:}} \cr
& {\text{Vertices }}\left( { - a,0} \right){\text{ and }}\left( {a,0} \right) \cr
& {\text{Vertices }}\left( { - \sqrt {14} ,0} \right){\text{ and }}\left( {\sqrt {14} ,0} \right) \cr
& {\text{Foci }}\left( { - c,0} \right){\text{ and }}\left( {c,0} \right) \cr
& {\text{Foci }}\left( { - \sqrt {34} ,0} \right){\text{ and }}\left( {\sqrt {34} ,0} \right) \cr
& {\text{Asymptotes: }}y = \frac{b}{a}x{\text{ and }}y = - \frac{b}{a}x \cr
& {\text{Asymptotes: }}y = \frac{{2\sqrt 5 }}{{\sqrt {14} }}x{\text{ and }}y = - \frac{{2\sqrt 5 }}{{\sqrt {14} }}x \cr
& \cr
& {\text{Graph}} \cr} $$
