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.
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.
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