Question 1191090
{{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}

given: 
Center at ({{{2}}},{{{2}}})=>{{{h=2}}}, {{{k=2}}}
a focus at ({{{10}}},{{{2}}})=> focus is  ({{{h - c}}}, {{{k }}}) =  ({{{10}}},{{{2}}})=>{{{2 - c=10}}}=>{{{2-10=c}}}=>{{{c=-8}}}
a vertex at ({{{5}}},2).=>   ({{{h + a}}}, {{{k}}}) = ({{{5}}}, {{{2}}})=>{{{2 + a=5}}}=>{{{a=2-5}}}=>{{{a=-3}}}

{{{b^2=c^2-a^2}}}
{{{b^2=(-8)^2-(-3)^2}}}
{{{b^2=64-9}}}
{{{b^2=55}}}

equation is:

{{{(x-2)^2/9-(y-2)^2/55=1}}}


{{{ drawing( 600, 600, -10, 15, -10, 10,
circle(2,2,.12),locate(2,2,C(2,2)),
circle(10,2,.12),locate(10,2.3,F(10,2)),
circle(5,2,.12),locate(5,2,V(5,2)),
graph( 600, 600, -10, 15, -10, 10, (1/3 )(6 - sqrt(55) sqrt(x^2 - 4x - 5)), (1/3)(sqrt(55) sqrt(x^2 - 4x - 5) + 6)  )) }}}