Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If the ellipse is placed on a large coordinate grid with its center at (0, 0), the equation x^2/2500+y^2/8100=1
models the path of the track. The units are given in yards. How long is the major axis of the track? Explain how you found the distance.
The equation of the ellipse is in standard form:
x^2/a^2 + y^2/b^2 = 1
Where a is the length of the semi-major axis (major axis) and b is the length of the semi-minor axis (minor axis).
In this case, a = 50 yards (the square root of 2500) and b = 90 yards (the square root of 8100).
The major axis is twice the length of the semi-major axis, so the length of the major axis is 2a = 2*50 = 100 yards.
Therefore, the length of the major axis of the track is 100 yards.