Question

OPTION 2 Centuries ago tunnels were built in semi-elliptical form. Will a truck 10' wide and 12' tall fit through an elliptical tunnel 30' wide and 13' tall on a two-lane road? Draw a picture of the conic on the Cartesian plane

Answer 1

Equation of the ellipse is x^2/15^2 + y^2/13^2 = 1. We find the corresponding x-coordinates if the y-coordinate is 12. Plugging y = 12 in the equation we get x^2/15^2 = 1 - 12^2/13^2 = 5^2/13^2 = > x/15 = plusminus 5/13 = > x = plusminus 5.15/13 = plusminus 5.77 Hence the distance between two points is 5.77 -(-5.77) = 11.54. Hence if the truck has to go in one of the lane then it will hit the bridge.