Question 1008677

{{{9x^2 - 4y^2 - 36= 0}}} 

{{{9x^2 - 4y^2 = 36}}} 

{{{9x^2/36 - 4y^2/36 = 36/36}}} 

{{{cross(9)x^2/cross(36)4 - cross(4)y^2/cross(36)9 = 1}}} 

{{{x^2/4 - y^2/9 = 1}}} 

here you have a hyperbola {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} and {{{h=0}}},{{{k=0}}},{{{a=2}}}, and {{{b=3}}}

so, the center is at origin  ({{{0}}},{{{ 0}}})
semi-major axis length:{{{a= 2}}}
semi-minor axis length:{{{b= 3}}}
vertices: 
({{{-a}}}, {{{0}}})  and  ({{{a}}}, {{{0}}})
({{{-2}}}, {{{0}}})  and  ({{{2}}}, {{{0}}})


foci:(c, 0) and (-c, 0)

{{{c^2=a^2+b^2}}}

{{{c^2=4+9}}}

{{{c^2=13}}}

{{{c=sqrt(13)}}}
 ({{{sqrt(13)}}},{{{ 0}}})  and  ({{{-sqrt(13)}}},{{{ 0}}})

or  ({{{3.6}}},{{{ 0}}}) and ({{{-3.6}}}, {{{0}}})


{{{ graph( 600, 600, -10, 10, -10, 10, sqrt((9x^2 -36)/4),-sqrt((9x^2 -36)/4)) }}}