(a)

The room with an elliptical ceiling.

Centered at the origin and that the major axis is horizontal.

The length of the room is .

.

The width of the room is .

.

The standard form of horizontal ellipse is .

Substitute , and in .

.

The equation of ellipse is .

(b)

To find the location of the foci, find .

In horizontal ellipse, .

Substitute and in .

.

So, the foci are about on either side of the center along the major axis.

(c)

The length of the segment between the foci is .

So, is about .

(a) The equation of ellipse is .

(b) Foci are about on either side of the center along the major axis.

(c) .