Question

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
(x + 8)² + (y + 9)² = 25
(x + 9)² + (y + 8)² = 3

Answer 1

(x – 8)² + (y – 9)² = 3
(x – 8)² + (y – 9)² = 14
are the correct answers

Answer 2

As given Concentric circles are those circles having same center but having different radii.

General equation of Circle → (x-a)² + (y-b)² = r², Center = (a,b),Radius = r

1. x ²+ y² = 25

→ ( x-0) ²+ (y-0)² = 5²  , center  = (0,0), Radius = 5

2.(x – 8)² + (y – 9)² = 3

→(x – 8)² + (y – 9)² = (√3 )², Center =(8,9), Radius = √3

3.  (x – 8)² + (y – 9)² = 14

→ (x – 8)² + (y – 9)² = [√14]², center = (8,9),Radius = √14

4. (x – 8)² + (y + 9)² =

→ (x – 8)² + (y + 9)² = [√3]², Center = (8,9), Radius = √3

5. (x + 8)² + (y + 9)² = 25

→(x + 8)² + (y + 9)² = 5² , Center = (-8,-9),Radius = 5

6. (x + 9)² + (y + 8)² = 3

→(x + 9)² + (y + 8)² = [√3]², Center = (-9,-8), Radius = √3

⇒Circle (2)→(x – 8)² + (y – 9)² = (√3 )², Center =(8,9), Radius = √3 and Circle 3 which is → (x – 8)² + (y – 9)² = [√14]², center = (8,9),Radius = √14 are Concentric.