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: