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 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.

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Answer 1

To find the length of the major axis of the track, we need to determine the distance between the two points on the ellipse that lie on the major axis.

First, let's find the coordinates of the points where the ellipse intersects the major axis.
To do this, we set y = 0 in the equation x^2/2500 + y^2/8100 = 1:
x^2/2500 + 0 = 1
x^2 = 2500
x = ±50

So, the points where the ellipse intersects the major axis are (50, 0) and (-50, 0).

Now, we can calculate the distance between these two points using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((50 - (-50))^2 + (0 - 0)^2)
d = √(100^2 + 0)
d = √10000
d = 100

Therefore, the length of the major axis of the track is 100 yards.