Question

A railroad tunnel is shaped like a semiellipse as shown below.



The height of the tunnel at the center is 58 ft and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.

Answer 1

@zpupster

Answer 2

@kirbykirby

Answer 3

@satellite73

Answer 4

b = 58, a is unknown, and the point (21,29) is on it
let the equation be
equation of ellipse:
x^2/a^2 + y^2/b^2= 1

x^2/a^2 + y^2/58^2 = 1
21^2/a^2 + 29^2/58^2 = 1
441/a^2 = 1 - 841/3364
441/a^2 = 3/4
3a^2 = 1764
a^2 = 588

x^2/588 + y^2/3364 = 1