24
QuizMultiple Choice

Circles — Test

Question 24 • TPS EdX Geometry

Consider a circle whose equation is x squared plus y squared minus 2 x minus 8 is equal to 0 Which statements are true? Choose three correct answers.

Answer
A
The center of the circle lies on the y -axis.
B
The radius of the circle is 3 units.
C
The center of the circle lies on the x -axis.
D
The radius of this circle is the same as the radius of the circle whose equation is x squared plus y squared is equal to 9 .
E
The standard form of the equation is open paren x minus 1 close paren squared plus y squared is equal to 3 .

Explanation

Complete the square in x: x² − 2x = (x − 1)² − 1. The equation becomes (x − 1)² + y² = 9, so the center is (1, 0) and the radius is 3. Thus, the radius is 3 units (B), the center lies on the x-axis (C), and the radius matches the circle x² + y² = 9 (D).

AI-written and checked against the verified answer.

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