A railroad tunnel is shaped like a semiellipse The height of

A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 15 ft and the vertical clearance must be 9 ft at a point 20 ft from the center. Find an equation for the ellipse.

Solution

ANS: x²/625 +y²/225=1 the equation of the ellipse will be of the form x²/a2 +y²/b²=1 hereb=15 asit passes through (20,9) therefore 20²/a²+9² /15²=1 hence 400/a²+81/225=1hence 400/a2=1-81/225 or400/a²=144/225 taking positive value for square root on both sides we get 20/a=12/15 hence a=25 the equation is x²/25²+y²/15²=1