Question 1132595
Find the hyperbola equation with Center ({{{6}}},{{{0}}}) ,
focal axis parallel to the x axis, and asymptotes {{{5x-6y-30=0}}}, {{{5x+6y-30=0}}} 

general formula:

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

with Center ({{{6}}},{{{0}}})


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


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

recall:
center: ({{{h}}},{{{k}}})
foci:( {{{h -c}}}, {{{k}}})
vertices: ({{{h -a}}}, {{{k}}})
equation of transverse axis:  {{{y=k}}}

The equations of the asymptotes of any hyperbola can be determined by a
translation of the graph to a center at ({{{h}}}, {{{k}}}).

{{{y -k}}} =±{{{(b/a)(x -h)}}}


if asymptotes:

{{{5x-6y-30=0}}} =>{{{6y=5x-30}}}=>{{{y=(5/6)x-6}}}
{{{5x+6y-30=0}}} =>{{{6y=-5x+30}}}=>{{{y=-(5/6)x+6}}}

=>{{{(b/a)=(5/6)}}}
=>{{{b=5}}} and {{{a=6}}}
 
so, your equation is:

{{{(x-6)^2/6^2-y^2/5^2  =1}}}