Question

On the lacrosse field, the circular region around the net, called the crease, is an area that only the goalie is allowed to be in. The crease is 18 feet in diameter. If the goalie is centered in the crease located at (30, 15) on the coordinate plane, what is the equation of the crease?

Answer 1

$\lparen x-30)^{\text{ }}\text{ + \lparen y-15\rparen = 9}$

Explanation:

The equation form of a circle is given by

$\lparen x-h)^2+\text{ \lparen y-k\rparen}^2\text{ = r}^2$

with

(h,k) being the coordinates of the center of the circle : (30, 15)

and r being the radius of the circle: 18 / 2 = 9

$\begin{gathered} \operatorname{\lparen}x-30)^2\text{ + \lparen y - 15\rparen}^2\text{ = 9}^2 \\ \sqrt{\operatorname{\lparen}x-30)^2}\text{ + }\sqrt{\left(y-15\rparen^2\right?}\text{ = }\sqrt{81} \\ \lparen x-30)\text{ + \lparen y-15\rparen = 9} \end{gathered}$