How do you write an equation for an ellipse given endpoints of the major axis at (2,2) and (2,-10) and endpoints of the minor axis at (0,-4) and (4,-4)?

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Answer 1 · 2017-01-16T05:30:45

$(x-2)^2/16+(y+3)^2/36=1$

Refer the graph

Find the center of the ellipse

$(x,y)=(2+2)/2,(2+(-10))/2=2,-5$

The Ellipse center is $(2, -3)$ ; the ellipse is vertical; hence its equation must be

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

$(h,k) = (2,-3)$

$a$ is the major axis

$b$ is the minor axis

$a=6$
$b=4$

Then the equation is -

$(x-2)^2/4^2+(y+3)^2/6^2=1$
$(x-2)^2/16+(y+3)^2/36=1$