The height of the tunnel at the center is 54 ft and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.

Question

goformit100 · Answer

Madam Can I Help you?

anonymous · Answer

You can! @goformit100

nurali · Answer

X^2/A^2 + Y^2/B^2 = 1
12^2/A^2 + (18/54)^2 = 1
144/A^2 = 1 - 1/9 = 8/9
A^2 = 9*144/8=162
Therefore the eq is
X^2/162 + Y^2/2916 = 1

anonymous · Answer

THANK YOU @Nurali

anonymous · Answer

wait a second that does not look correct when graphed! @Nurali

anonymous · Answer

It must look like this! @Nurali

nurali · Answer

http://www.wolframalpha.com/input/?i=X%5E2%2F162+%2B+Y%5E2%2F2916+%3D+1

anonymous · Answer

Oh I'm sorry! Mathway made it look funny :( @Nurali

nurali · Answer

no problem.