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)?

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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)?

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Answer 1 · 2016-10-28T05:06:01

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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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

Explanation:

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