SOLUTION: A racetrack is in the shape of an​ ellipse, 170 feet long and 40 feet wide. What is the width 10 feet from a​ vertex?

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Question 1154217: A racetrack is in the shape of an​ ellipse, 170 feet long and 40 feet wide. What is the width 10 feet from a​ vertex?
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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The semiaxes are 170/2 = 85 ft  and  40/2 = 20 ft.


The equation of the ellipse is


    x%5E2%2F85%5E2 + y%5E2%2F20%5E2 = 1.


From the equation,  


    y = +/- 20%2Asqrt%281+-+x%5E2%2F85%5E2%29.


Substitute here  x = 85-10 = 75. Then


    y = +/- 20%2Asqrt%281-%2875%2F85%29%5E2%29 = +/- 9.412  (rounded to 3 decimal places).


So, the answer to the problem's question is  9.412 - (-9.412) = 2*9.412 = 18.824 ft  (rounded).    ANSWER

Solved.