SOLUTION: An elliptical arch bridge is build across a one lane highway. The arch is 20ft across an has a maximum center height of 12ft Will a farm truck hauling a load l0ft wide with a clear

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Question 1196661: An elliptical arch bridge is build across a one lane highway. The arch is 20ft across an has a maximum center height of 12ft Will a farm truck hauling a load l0ft wide with a clearance height of 11ft be able to go through the bridge without damage?
Answer by Alan3354(69443) About Me  (Show Source):
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An elliptical arch bridge is build across a one lane highway. The arch is 20ft across an has a maximum center height of 12ft Will a farm truck hauling a load l0ft wide with a clearance height of 11ft be able to go through the bridge without damage?
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Three points are given:
(-10,0), (0,12) and (10,0)
One ellipse thru the 3 points is x%5E2%2F100+%2B+y%5E2%2F144+=+1
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x%5E2%2F100+%2B+y%5E2%2F144+=+1
At x = -5 for +5:
25%2F100+%2B+y%5E2%2F144+=+1
y%5E2%2F144+=+3%2F4
y%5E2+=+108
y =~ 10.39 so there is clearance.