Question 1198497: a jogging path is in the shape of an ellipse. if it is 100ft long and 50ft wide, what is the width of the track 20ft from either vertex Answer by ikleyn(52886) (Show Source):
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a jogging path is in the shape of an ellipse.
if it is 100ft long and 50ft wide, what is the width of the track 20ft from either vertex
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Major semi-axis is a = 100/2 = 50 ft long.
Minor semi-axis is b = 50/2 = 25 ft long.
The equation of the ellipse is
+ = 1.
20 ft from the vertex is x= 50-20 = 30 ft from the center at the major semi-axis.
Substitute x= 30 into equation
+ = 1,
or
= 1 - = 1 - = 1 - = .
Hence, = +/- = +/- .
It implies y = +/- = +/- 20.
It means that the width of the track is 20 + 20 = 40 ft there. ANSWER
