How do I find the foci of an ellipse if its equation is #x^2/16+y^2/36=1#?

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Answer 1 · 2014-10-04T21:30:59

#x^2/16+y^2/36=1#

#a^2=36#
#b^2=16#

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=36-16#
#c^2=20#
#c=sqrt(2*2*5)#
#c=2sqrt(5)#

The coordinates for the foci are #(0,+-c) -> (0,+-2sqrt(5))#