A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch.
A) $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 729 } = 1$
B) $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 144 } = 1$
C) $\frac { x ^ { 2 } } { 729 } + \frac { y ^ { 2 } } { 144 } = 1$
D) $\frac { x ^ { 2 } } { 54 } + \frac { y ^ { 2 } } { 729 } = 1$
E) $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 729 } = 1$

Question

A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 54 feet and a height at the center of 12 feet.Find an equation of the semielliptical arch. ​
A) $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 729 } = 1$
B) $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 144 } = 1$
C) $\frac { x ^ { 2 } } { 729 } + \frac { y ^ { 2 } } { 144 } = 1$
D) $\frac { x ^ { 2 } } { 54 } + \frac { y ^ { 2 } } { 729 } = 1$
E) $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 729 } = 1$

Quizplus · Accepted Answer

The equation of a semielliptical arch is given by:
((x/a)^2 + (y/b)^2 = 1)
where, 
a = major axis/2 = 54/2 = 27
b = height at the center = 12
So the equation of the semielliptical arch is:
((x/27)^2 + (y/12)^2 = 1)
which is option C.

A Semielliptical Arch Over a Tunnel for a One-Way Road x2144−y2729=1\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 729 } = 1144x2​−729y2​=1

A Semielliptical Arch Over a Tunnel for a One-Way Road $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 729 } = 1$