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? Explain how you found the distance.
To determine the length of the major axis of the elliptical track, we need to first identify the key elements of the given equation of the ellipse:
The general form of the equation of an ellipse centered at the origin is:
(x^2/a^2) + (y^2/b^2) = 1
Here, a represents the length of the semi-major axis (half of the major axis), and b represents the length of the semi-minor axis (half of the minor axis).
Comparing the given equation x^2/22500 + y^2/28100 = 1 with the general form, we see that a^2 = 22500 and b^2 = 28100.
To find the length of the major axis, we need to first find the lengths of the semi-major axis (a) and then multiply it by 2.
a^2 = 22500
a = √22500
a = 150
The length of the major axis is twice the length of the semi-major axis, so:
Major Axis = 2a
= 2(150)
= 300 yards
Therefore, the length of the major axis of the elliptical track is 300 yards.