A certain bridge arch is in the shape of half an ellipse 106 feet wide and 25.1 feet high. At what horizontal distance from the center of the arch is the height equal to 15.1 feet?

Answer 1

From the description, this is a horizontal ellipse with the semi-major axis of 53 feet, and a semi-minor axis of 25.1 feet. If we put the center at (0,0), then this is the equation of the ellipse:

x² / 53² + y² / 25.1² = 1

Always draw a picture for a problem like this

Plug in the given value for the height ( y = 15.1 ), and solve for x.