Question

Locate the foci of the ellipse. Show your work.? (x^2/36)+ (y^2/11) =1

Answer 1

See below

Explanation:

`(x^2/36)+ (y^2/11) =1` is the equation

The standard form for a horizontal ellipse is:
`((x-h)^2/a^2)+ ((y-k)^2/b^2) =1`

To find `c` which is the distance from the center of the ellipse to one of the fociis, determine the center first `(h,k)`, since the values of that are `0`, the ellipse has a center at the point of origin

To determine `c`, use:
`c^2=a^2-b^2`

`c= +-sqrt(36-11)`

`c=+-5`

So the focii are at `(5, 0)` and `(-5,0)`