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.

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. ​

Quizplus · Accepted Answer

The equation of a semi-elliptical arch with major axis a and height at the center b is given by:
(x/a)^2+(y/b)^2=1
Plugging in the given values, we get:
(x/27)^2+(y/12)^2=1
Multiplying by 27^2 and rearranging, we get the semi-elliptical arch equation in standard form:
729x^2+1458y^2=23328

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