Question 720389
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.<br>
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<br>
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}}}