find the width of an arch using ellipse formula

Question

A bridge has an arch that is in the shape of the top half of an ellipse. The equation of this semi-ellipse, where x and y are measured  in ft. is x^2/225+y^2/100=1. Determine the width of the arch.

Answer 1

The semi-ellipse at its widest point is the length of its major axis. In the equation of the ellipse the square root of the reciprocal of the coefficient of the x^2 term is the square of the semimajor axis. So 225 is the square of the length of the semimajor axis, with square root 15 feet. The major axis, therefore, has length 30 feet, so this is the width of the bridge.