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. show work
To find the length of the major axis of the elliptical track, we first need to determine the length of the major axis. The major axis of an ellipse is the longest diameter of the ellipse and passes through the center.
The equation of an ellipse in standard form is:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Where (h, k) is the center of the ellipse, a is the length of the major axis, and b is the length of the minor axis.
Comparing the given equation x^2/2500 + y^2/8100 = 1 to the standard form, we can see that:
a^2 = 2500
a = √2500
a = 50 yards
Therefore, the length of the major axis of the elliptical track is 100 yards. This was found by taking the square root of 2500, which gives us the length of the major axis.