A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 20 feet and a height at the center of 4 feet.Select the arch of the tunnel on a rectangular coordinate system with the center of the road entering the tunnel at the origin.Identify the coordinates of the known points.
A)
B)
C)
D)

Question

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 20 feet and a height at the center of 4 feet.Select the arch of the tunnel on a rectangular coordinate system with the center of the road entering the tunnel at the origin.Identify the coordinates of the known points. ​
A)​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

Since the major axis is 20 feet and the height at the center is 4 feet, the semi-ellipse can be modeled by the equation:
$\frac{x^2}{10^2}+\frac{y^2}{2^2}=1$

Since the center of the road entering the tunnel is at the origin, we can conclude that the coordinates of the known points are:
(-10,0) and (10,0) for the endpoints of the major axis, and (0,2) and (0,-2) for the endpoints of the minor axis.

Therefore, the correct choice is B, which shows the semi-ellipse centered at the origin of the rectangular coordinate system with the known points highlighted.

A Semielliptical Arch Over a Tunnel for a One-Way Road