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

B) (x – 8)² + (y – 9)² = 3

C) (x – 8)² + (y – 9)² = 14

are the correct answers

Explanation:

Answer 2

(a) (x -8)² +(y -9)² = 3

(b) (x -8)² +(y -9)² = 14

Explanation:

The attached graph shows the circle center has coordinates (8, 9). The standard-form equation for a circle with center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

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Any concentric circle will have the same center, so will have an equation of the form ...

(x -8)² +(y -9)² = constant

The answer choices that match this form are ...

• (x -8)² +(y -9)² = 3
• (x -8)² +(y -9)² = 14

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Additional comment

The given circle has a radius of 5, so its "constant" is 5² = 25. The answer choices have different constants, so represent concentric circles, not coincident circles, as required.