How do you write an equation of an ellipse in standard form with foci (0,+/- 4) and co-vertices at (+/- 4,0)?

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Answer 1 · 2017-03-27T12:56:41

The equation is #y^2/32+x^2/16=1#

This is an ellipse with the major axis vertical.

The center is #=(0,0)#

The equation is

#y^2/a^2+x^2/b^2=1#

#b=4#

#c=4#

#a^2=b^2+c^2#

#=16+16=32#

The equation is

#y^2/32+x^2/16=1#

graph{(y^2/32+x^2/16-1)=0 [-15.55, 12.92, -8.17, 6.06]}