Question

17. The Colosseum in Rome was the largest amphitheater built in the Roman Empire. The interior of the Colosseum is a perfect circle. The roof of this enormous amphitheater was about 600 feet in diameter. If the center of the Colosseum is assumed to be at origin, then write an equation for the circle that represents the roof of the Colosseum.

Answer 1

`(x)^(2)+(y)^(2)=90,000`

Explanation:

we know that

The equation of the circle (the roof of the Colosseum) in standard form is equal to

`(x-h)^(2)+(y-k)^(2)=r^(2)`

where

(h,k) is the center and r is the radius

we have

(h,k)=(0,0) ----> is the origin

`r=600/2=300\ ft` ----> the radius is half the diameter

substitute

`(x-0)^(2)+(y-0)^(2)=300^(2)`

`(x)^(2)+(y)^(2)=90,000`