To find the length of the major axis of the elliptical track, we first need to understand the equation of an ellipse in standard form:
(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 semi-major axis, and 'b' is the length of the semi-minor axis.
From the given equation 2500 + 8100 = 1, we can see that this ellipse equation is not in standard form.
To convert the given equation into standard form, we have to divide both sides of the equation by 8100:
(2500/8100) + (y^2/8100) = 1,
0.3086 + (y^2/8100) = 1,
y^2 = 8100*(1 - 0.3086)
y^2 = 5541.4
Since the equation represents the y^2 value, and we are asked to find the length of the major axis, we need to find the value of 'y' for y^2 = 5541.4 :
y = sqrt(5541.4)
y ≈ 74.49
The length of the major axis of the track is equal to 2*semi-major axis = 2*y ≈ 2*74.49 ≈ 148.98 yards.
Therefore, the length of the major axis of the elliptical track is approximately 148.98 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 y? equation
2500 + 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.
1 answer