How do you write an equation of an ellipse given endpoints of major axis at (2,12) and (2,-4) and endpoints of the minor axis at (4,4) and (0,4)?

1 Answer
Apr 29, 2017

Answer:

The equation is #(y-4)^2/64+(x-2)^2/4=1#

Explanation:

The equation of an ellipse with a vertical major axis is

#(y-h)^2/a^2+(x-k)^2/b^2=1#

The length of the major axis is #a=(12-(-4))/2=8#

The length of the minor axis is #b=(4-0)/2=2#

The center of the ellipse is #(h,k)=(2,4)#

The equation of the ellipse is

#(y-4)^2/64+(x-2)^2/4=1#

graph{(y-4)^2/64+(x-2)^2/4=1 [-28.65, 29.11, -14.68, 14.2]}