Hello, JROD23!

The ellipse problem is not pretty . . .

2. Given the ellipse equation: .

find the coordinates of the center, the vertices, and the foci.

Sketch the ellipse.

To get Standard Form, we must complete-the-square.

We are given: .

. . . . .

. . . .+ 1+ 4+ 9+ 16

. . . . . . . . . . .

Divide by 25: .

And we have: . .

This is a "vertical" ellipse. .Its center is:

. . The major axis is vertical: .

. . The minor axis is horizontal: .

The vertices (ends of the major axis) are units above and below the center.

. . Vertices:

The co-vertices (ends of the minor axis) are units left and right of the center.

. . Covertices:

The foci are above and below the center. .We must find .

We have: .

. . Foci: