Question

ntric Circles
On a coordinate plane, a circle has a center at (8, 9).

Concentric circles are circles with the same center but different radii. Which equations represent concentric circles along with the circle shown in the graph? Check all that apply.

x2 + y2 = 25
(x – 8)² + (y – 9)² = 3
(x – 8)² + (y – 9)² = 14
(x – 8)² + (y + 9)² = 3

Answer 1

Concentric circles share the same center (h, k). The standard form is (x − h)^2 + (y − k)^2 = r^2. The given circle has center (8, 9), so only equations with (x − 8)^2 + (y − 9)^2 = ... are concentric.

Correct choices:
- (x − 8)^2 + (y − 9)^2 = 3
- (x − 8)^2 + (y − 9)^2 = 14

x^2 + y^2 = 25 has center (0,0), and (x − 8)^2 + (y + 9)^2 = 3 has center (8, −9), so they are not concentric.