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QUESTION

# 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))