Consider a circle whose equation is x2 + y2 + 4x – 6y – 36 = 0. Which statements are true? Check all that apply.To begin converting the equation to standard form, subtract 36 from both sides.To complete the square for the x terms, add 4 to both sides.The center of the circle is at (–2, 3).The center of the circle is at (4, –6).The radius of the circle is 6 units.The radius of the circle is 49 units.
Answer
A
To begin converting the equation to standard form, subtract 36 from both sides.
B
To complete the square for the x terms, add 4 to both sides.
C
The center of the circle is at (–2, 3).
D
The center of the circle is at (4, –6).
E
The radius of the circle is 6 units.
F
The radius of the circle is 49 units.
Explanation
Move the constant term to the right: x² + 4x + y² − 6y = 36. Completing the square for x² + 4x requires adding (4 ÷ 2)² = 4; completing the square for y² − 6y requires adding (−6 ÷ 2)² = 9, giving (x + 2)² + (y − 3)² = 49. The center is (−2, 3), so statement C is true; the radius is √49 = 7, not 6 or 49.
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