How do I find the foci of an ellipse if its equation is ##x^2/36+y^2/64=1##?

##x^2/36+y^2/64=1##

##a^2=64## ##b^2=36##

The center is ##(0,0)##.

The y-axis is the major axis. We know this because the ##y^2## term has the larger denominator.

We find the foci using the following equation and solving for ##c##.

##c^2=a^2-b^2## ##c^2=64-36## ##c^2=28## ##c=sqrt(2*2*7)## ##c=2sqrt(7)##

The coordinates for the foci are ##(0,+-c) -> (0,+-2sqrt(7))##