Question

Question #d2701

Answer 1

`color(red)((x-4)^2/3^2+(y+1)^2/2^2=1)`

Explanation:

We are to find out the Standard from of an ellipse

`"with vertices at "(1, -1) and (7, -1)`

`"and foci at "(4+sqrt5, -1) and (4-sqrt5, -1)`

`"Center"->(4,-1)" and semi major axis"(a)=(7-1)/2=3`

Now if e be eccentricity and b be the semi minor axis of the ellipse then `e^2=(a^2-b^2)/a^2=>a^2e^2=a^2-b^2`

`"The distance of focus from center"=ae=4+sqrt5-4=sqrt5`

`=>a^2e^2=5=>a^2-b^2=5`

`=>3^2-b^2=5`

`=>b^2=9-5=4=>b=2`

So the equation of the ellipse having center`(4,-1)` and semi major axis `a=3` and semi minor axis (b=2)

`color(red)((x-4)^2/3^2+(y+1)^2/2^2=1)`