Question

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 (the drawing ^) 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.

Answer 1

Given:
center (0,0)
the equation given should have been:
x²/2500 + y²/8100 = 1

We need to identify the larger denominator. If it is under x, the ellipse is horizontal. If it is under y, the ellipse is vertical. In this case, 8100 is larger and it is under y so the ellipse is vertical.

(x-h)²/b² + (y-k)²/a² = 1

h and k are the center values which are both 0.
a = length of the semi-major axis
b = length of the semi-minor axis

x²/2500 + y²/8100 = 1
x²/50² + y²/90² = 1

a = 90. It is the semi-major axis. 

length of the major axis is 180yards.

90 x 2 = 180