Question 1187159
Write the equation of the hyperbola given the following information 

Vertices : ({{{2}}}, {{{-6}}}); ({{{-4}}}, {{{-6}}}) 
Foci: ({{{-1 + sqrt(10)}}}, {{{- 6}}}), ({{{-1-sqrt(10)}}}, {{{- 6}}})

the canter is half way between

({{{h}}},{{{k}}})=({{{(2-4)/2}}},({{{-6-6)/2}}})=({{{-1}}},{{{-6}}})


{{{a=distance from the center to vertex}}}

=>{{{a=3}}}

Foci: ({{{-1 + sqrt(10)}}}, {{{- 6}}}), ({{{-1-sqrt(10)}}}, {{{- 6}}})

{{{c}}}=distance from the center to foci

{{{c=sqrt((- 1 + sqrt(10)+1)^2(-6+6)^2)=sqrt( 10)}}}
{{{c=sqrt(10)}}}

{{{b=sqrt(c^2-a^2)}}}
{{{b=sqrt((sqrt( 10))^2-3^2)}}}
{{{b=sqrt(10-9)}}}
{{{b=sqrt(1)}}}
{{{b=1}}}


your equation is:

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

{{{(x-2)^2/3^2-(y-(-6))^2/1^2=1}}}

{{{(x-2)^2/9-(y+6)^2=1}}}