Question 1198403
The equation of a hyperbola is 
 
{{{(x-h)^2/a^2 - (y-k)^2 /b^2=1}}}, where ({{{h}}},{{{k}}}) is the center, {{{a}}} and {{{b}}} are the lengths of the semi-major and the semi-minor axes.

given:
Vertices: ({{{13}}},{{{0}}}), ({{{-1}}},{{{0}}}) 

asymptotes: {{{y = x - 6}}} and {{{y = -x + 6}}}

Vertices  are at  ({{{h+-a}}},{{{k}}})

so,   {{{k=0}}}  

{{{h+a=13}}}....eq.1
{{{h-a=-1}}}.....eq.2
--------------------add
{{{2h=12}}}
{{{h=6}}}

the center is at ({{{6}}},{{{0}}}) 

the
{{{6+a=13}}}
{{{a=13-6}}}
{{{a=7}}}

take into account different properties of a hyperbola:

{{{b/a=1}}}
{{{b/7=1}}}
{{{b=7}}}

the equation of hyperbola is:

{{{(x-6)^2/7^2 - (y-0)^2 /7^2=1}}}

{{{(x-6)^2/49 - y^2 /49=1}}}



{{{ drawing( 600, 600, -10, 20, -15, 15,
circle(13,0,.12),circle(-1,0,.12),
locate(13,1,v(13,0)),locate(-1,1,v(-1,0)),

graph( 600, 600, -10, 20, -15, 15, -x + 6,x - 6,-sqrt(x^2-12x-13), sqrt(x^2-12x-13))) }}}