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.

choices are in the attachment

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:

(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1  for ellipses with horizontal major axes and

x-h)^2 / b^2 + (y-k)^2 / a^2 = 1   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:

(x-0)^2 / (40)^2 + (y-0)^2 / (36)^2 = 1

which simplifies to:
x^2 / 1600 + y^2 / 1296 = 1

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