Posted by Stacey grahaM on Sunday, May 2, 2010 at 4:53pm.
A railroad tunnel is shaped like semiellipse. The height of the tunnel at the center is 69 ft and the vertical clearance must be 23 ft at a point 16ft from the center. Find an equation for the ellipse.

Trig  Reiny, Sunday, May 2, 2010 at 5:20pm
b = 69, a is unknown, and the point (16,23) is on it
let the equation be
x^2/a^2 + y^2/69^2 = 1
16^2/a^2 + 23^2/69^2 = 1
256/a^2 = 1  529/4761
256/a^2 = 8/9
8a^2 = 2304
a^2 = 288
x^2/288 + y^2/4761 = 1
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