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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
Solved.