Trig

A railroad tunnel is shaped like semi-ellipse. 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.

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  1. 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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