How do you find the coordinates of the center, foci, lengths of the major and minor axes given #y^2/18+x^2/9=1#?

1 Answer
Nov 11, 2016

The center is #=(0,0)#
The lengh of the major axis is #=6sqrt2#
The length of the minor axis is #=6#

Explanation:

The general equation of the ellipse is
#(y-h)^2/a^2+(x-k)^2/b^2=1#
The center is #=(k,h)#

The foci are #(k,h+-c)#

The center is #=(0,0)#
The lengh of the major axis is #=2*sqrt18=6sqrt2#
The length of the minor axis is #=2sqrt9=6#
To determine the foci, we need #c=sqrt(18-9)=3#
Therefore, the foci are F#=(0,3)# and F'#(0,-3)#

graph{(y^2/18)+(x^2/9)=1 [-11.25, 11.25, -5.625, 5.625]}