SOLUTION: Find the foci of the ellipse whose major axis has endpoints $(0,0)$ and $(13,0)$ and whose minor axis has length 12. Enter your answer as a list of pairs separated by commas.

Question 1074902: Find the foci of the ellipse whose major axis has endpoints $(0,0)$ and $(13,0)$ and whose minor axis has length 12.
Enter your answer as a list of pairs separated by commas.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The center of that ellipse is the midpoint of the major axis,
half way between (0,0) and (13,0) on line y=0.
The coordinates of that midpoint are the averages of the coordinates of the vertices.
The midpoint is (6.5,0) , and that is the center of the ellipse.
The distance from the center to each vertex is called the semi-major axis and represented as .
In this case .
Half of the minor axis is called the semi-minor axis and is represented with .
That is the distance from the center to each co-vertex.
In this case .
The distance from the center to each focus is represented with ,
and is related to and by .
In this case .
Solving for :

A calculator can do that, but I don't need one

.
That is the distance from center (6.5,0) to each focus.
The foci are on the same line as the vertices, line y=0,
on either side of the center,
so the x-coordinate of one focus is ,
and the x-coordinate of the other focus is .
So, the foci are .
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