Solving Problems Involving Different Conic Sections

Question

A tunnel through a mountain for a four-lane highway is to have an elliptical opening. The total width of the highway (not the opening) is to be 16m, and the height at the edge of the road must be sufficient for a truck 4m high to clear if the highest point of the opening is to be 5m approximately. How wide must the opening be?

Answer 1

Equation of ellypse: x²/a² + ,y²/25 = 1;. For x = 8m y = 4m. So, 64/a² + 16/25 = 1; 64/a² = 9/25; a = 40/3m.

So, width of tunnel 2a = 80/3m = 26.67m