Question

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 (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

Explanation:

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Answer 2

Correct options:

(x – 8)² + (y – 9)² = 3

(x – 8)² + (y – 9)² = 14

Explanation:

If the circle has a center at (8,9), the equation for this circle is:

`(x-8)^2 + (y - 9)^2 = r^2`

All concentric circles have the same center, so their equations need to have the same left side of the equation above.

-> x2 + y2 = 25

This circle has a center at (0,0), so it's not concentric to our circle.

-> (x – 8)² + (y – 9)² = 3

This circle has a center at (8,9), so it's concentric to our circle.

-> (x – 8)² + (y – 9)² = 14

This circle has a center at (8,9), so it's concentric to our circle.

-> (x – 8)² + (y + 9)² = 3

This circle has a center at (8,-9), so it's not concentric to our circle.

-> (x + 8)² + (y + 9)² = 25

This circle has a center at (-8,-9), so it's not concentric to our circle.

-> (x + 9)² + (y + 8)² = 3

This circle has a center at (-8,-9), so it's not concentric to our circle.

Correct options:

(x – 8)² + (y – 9)² = 3

(x – 8)² + (y – 9)² = 14