Ailani draws a map of her local town. She places the town hall at the origin of a coordinate plane and represents a lake with a circle drawn on the map. The center of the lake is 19 miles east and 3 miles south of the town hall, and the radius of the lake is 0 point 5 miles. If the positive x -axis represents east and the positive y -axis represents north, which equation represents the lake?
Answer
A
open paren x minus 19 close paren squared plus open paren y plus 3 close paren squared is equal to 0 point 5
B
open paren x plus 19 close paren squared plus open paren y minus 3 close paren squared is equal to 0 point 5
C
open paren x minus 19 close paren squared plus open paren y plus 3 close paren squared is equal to 0 point 2 5
D
open paren x plus 19 close paren squared plus open paren y minus 3 close paren squared is equal to 0 point 2 5
Explanation
A circle with center (h, k) and radius r has equation (x − h)² + (y − k)² = r². The lake’s center is 19 miles east and 3 miles south, so its coordinates are (19, −3); its radius squared is 0.5² = 0.25. Substituting gives (x − 19)² + (y + 3)² = 0.25, which is choice B.
AI-written and checked against the verified answer.