The arch of the bridge below is half an ellipse, a "semi-ellipse". The arch is 148m long and has a height of 48m at the center. The height of the arch is 10m at point p. What is the distance from p to the center?

3 answers

Draw a diagram.
Set the center of the ellipse at (0,0). Then we have semi-axes

a = 74
b = 48

x^2/74^2 + y^2/48^2 = 1

Now plug in y=10 and find x.

The distance d is then

d^2 = x^2 + 10^2
65561
how did you get the a=74???