SOLUTION: An elliptical track has a major axis that is 80 yards long and a minor axis that is 72 yards long. Find an equation for the track if its center is (0, 0) and the major axis is the

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Question 720389: An elliptical track has a major axis that is 80 yards long and a minor axis that is 72 yards long. Find an equation for the track if its center is (0, 0) and the major axis is the x-axis.
Answer by jsmallt9(3758) (Show Source):
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Since the major axis is 80 yards long, the distance from the center to a vertex on the major axis, which is the "a" in the equation, would be 40 yards. With similar logic we can find that the distance from the center to a vertex on the minor axis, "b" in the equation, would be 36 yards.

With the center, a and b we are just about ready to write the equation. The standard forms for equations of ellipses are:
for ellipses with horizontal major axes
and
for ellipses with vertical major axes

Since the major axis is the x-axis, which is horizontal, we will use the first form. Using the values we found for a and b and the x-coordinate of the center as "h" and the y-coordinate of the center as "k" we get:

which simplifies to: