Solve the problem.
-An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis)if the height 27 feet from the center is to be 16 feet above ground?
A)60.72 ft
B)30.36 ft
C)50.29 ft
D)118.13 ft

Question

Quizplus · Accepted Answer

The equation of an ellipse with its major axis along the y-axis and center at the origin is $x^2/b^2 + y^2/a^2 = 1$, where 2a is the length of the major axis and 2b is the length of the minor axis. Given that the top of the arch is 35 feet above the ground, the semi-major axis (a) is 35 feet. The point (27, 16) lies on the ellipse, where 16 feet is the height above the ground, meaning the y-coordinate is 35 - 16 = 19 feet from the center. Plugging these values into the ellipse equation, we solve for b, the semi-minor axis. The full span of the bridge (the length of the minor axis) is 2b. Using the given point to solve for b, we find that the span of the bridge is approximately 60.72 feet.

Solve the Problem. -An Arch for a Bridge Over a Highway Is in Highway