How do you write an equation of an ellipse given the endpoints of major axis at (10,2) and (-8,2), foci at (6,2) and (-4,2)?

1 Answer
Narad T.
Oct 28, 2016

The equation is #((x-1)^2)/81+((y-2)^2)/56=1#

Explanation:

We have here a horitontal major axis:
The center is #((10-8)/2,2)=(1,2)#
the major axis is #a=10-1=9#
The distance focus to center is #5#
So we can calculate b from #b^2=a^2-c^2#
#b^2=81-25=56#

The equation of the ellipseis #(x-h)^2/a^2+(y-k)^2/b^2=1#

here #(h,k)=()1,2# and #a=9# And #b=sqrt56#

So the equation is #((x-1)^2)/81+((y-2)^2)/56=1#

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