Question 1118335
{{{4x^2+9y^2=36}}}


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


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


note the relationship {{{x^2/a^2+y^2/b^2=1}}}, and there is a constant c so that {{{c^2=a^2-b^2}}}.

Your example has {{{c^2=9-4=5}}}
and from that, 
{{{c=sqrt(5)}}}.


Your foci each is  c=sqrt(5)  from the center of the ellipse and are along the long axis of the ellipse.


Major axis is horizontal, along the x-axis.


You have  {{{(x-0)^2/9+(y-0)^2/4=1}}} so the center point is  at  (0,0).
Foci are at  ( {{{-sqrt(5)}}}, 0 ) and ({{{sqrt(5)}}}, 0 ).