9
QuizMultiple Choice

Circles — Test

Question 9 • Math 3

Which equation represents the circle described? The radius is 2 units. The center is the same as the center of a circle whose equation is x squared plus y squared minus 8 x minus 6 y plus 24 is equal to 0

Answer
A
open paren x plus 4 close paren squared plus open paren y plus 3 close paren squared is equal to 2 squared
B
open paren x minus 4 close paren squared plus open paren y minus 3 close paren squared is equal to 2 squared
C
open paren x plus 4 close paren squared plus open paren y plus 3 close paren squared is equal to 2
D
open paren x minus 4 close paren squared plus open paren y minus 3 close paren squared is equal to 2

Explanation

Complete the square in x² + y² − 8x − 6y + 24 = 0: (x − 4)² + (y − 3)² = 1, so the center is (4, 3). A circle with that center and radius 2 has equation (x − 4)² + (y − 3)² = 2². Therefore, choice B is correct; the right side must be the radius squared, 4.

AI-written and checked against the verified answer.

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