Question 9377
{{{ 9 x^2 + 4 y^2 = 9}}}  


Divide both sides by 9:
{{{x^2 + (4y^2)/9 = 1}}}


Rewrite this as:
{{{(x^2)/1 + (y^2)/(9/4) = 1}}}


The center of the ellipse is at (0,0), and the radius in the x direction is 1, the radius in the y direction is {{{3/2}}}.  Therefore the major axis is in the Y-direction, and the foci will be on the y-axis at (0, c) and (0, -c), where {{{1^2 + c^2 = (3/2)^2}}}


Solve for c:
{{{1 + c^2 = 9/4}}}
{{{c^2 = 9/4 - 1}}}
{{{c^2 = 5/4}}}
{{{c =  (sqrt(5))/2 }}}  or {{{c = - (sqrt(5))/2}}}


Therefore, I have the foci at ( 0, {{{(sqrt(5))/2  }}}) and ( 0,{{{ -(sqrt(5))/2  }}}).


R^2 at SCC