Question 1068651: A tunnel is built under a river for a road 12 m. wide with a 2m. sidewalk on either side. The top of the tunnel is semi-elliptical. A local law stipulates that there must be a clearance of at least 3.6 m. at all points on the road. If the smallest possible ellipse is used, find the clearance at the center of the road. Show your illustrations.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! So choose a coordinate system so that the center of the road is (0,0).
The left side of the road is then (-6,0) and the right is (6,0).
The far left of the left sidewalk is (-8,0) and the far right of the right sidewalk is (8,0).
The points (-6,3.6) and (6,3.6) must be on your ellipse.
To make it the smallest ellipse, (-8,0) and (8,0) must also be on your ellipse.
Start with the general equation of an ellipse.
(8,0)
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(6,3.6)
So when, 
 
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