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

Oct 4, 2014

${x}^{2} / 36 + {y}^{2} / 64 = 1$

${a}^{2} = 64$
${b}^{2} = 36$

The center is $\left(0 , 0\right)$.

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 $c$.

${c}^{2} = {a}^{2} - {b}^{2}$
${c}^{2} = 64 - 36$
${c}^{2} = 28$
$c = \sqrt{2 \cdot 2 \cdot 7}$
$c = 2 \sqrt{7}$

The coordinates for the foci are $\left(0 , \pm c\right) \to \left(0 , \pm 2 \sqrt{7}\right)$