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?(x-15)2 + (y-30)2 = 18(x+15)2 + (y+15)2 = 81(x+30)2 + (y-15)2 = 9(x-30)2 + (y-15)2 = 81
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?(x-15)2 + (y-30)2 = 18(x+15)2 + (y+15)2 = 81(x+30)2 + (y-15)2 = 9(x-30)2 + (y-15)2 = 81
Solution
The equation of a circle in a coordinate plane is given by (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.
In this case, the center of the crease is at (30, 15) and the diameter is 18 feet. Therefore, the radius is half the diameter, which is 9 feet.
Substituting these values into the equation, we get:
(x-30)² + (y-15)² = 9²
So, the equation of the crease is (x-30)² + (y-15)² = 81.
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