note: Enter your answer and show all the steps that you use to solve this problem in the space provided.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 x22500+y28100=1 models the path of the track. The units are given in yards. How long is the major axis of the track? show work
To find the length of the major axis of the ellipse, we first need to identify the coefficients of x² and y² in the given equation of the ellipse x²/22500 + y²/28100 = 1.
The general form of the equation of an ellipse centered at the origin is x²/a² + y²/b² = 1, where a is the length of the semi-major axis and b is the length of the semi-minor axis.
Comparing the given equation x²/22500 + y²/28100 = 1 with the general form, we have:
a² = 22500
b² = 28100
Therefore, the length of the major axis (2a) is:
2a = 2√22500 = 2 * 150 = 300 yards
So, the length of the major axis of the elliptical track is 300 yards.