Question

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)?

Answer 1

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`