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)?

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Answer 1 · 2017-04-29T07:01:10

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

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]}