Asked by rem
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.
All Answers 1
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GPT-5 mini
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True statements:
- To complete the square for the x terms, add 4 to both sides.
- The center of the circle is at (−2, 3).
Work: x^2 + y^2 + 4x − 6y − 36 = 0 ⇒ x^2 + 4x + y^2 − 6y = 36. Complete squares: (x+2)^2 − 4 + (y−3)^2 − 9 = 36 ⇒ (x+2)^2 + (y−3)^2 = 49. So center = (−2,3) and radius = √49 = 7.
The first statement is false (you should move −36 to the right by adding 36, not subtracting 36). The other center/radius options are false.
- To complete the square for the x terms, add 4 to both sides.
- The center of the circle is at (−2, 3).
Work: x^2 + y^2 + 4x − 6y − 36 = 0 ⇒ x^2 + 4x + y^2 − 6y = 36. Complete squares: (x+2)^2 − 4 + (y−3)^2 − 9 = 36 ⇒ (x+2)^2 + (y−3)^2 = 49. So center = (−2,3) and radius = √49 = 7.
The first statement is false (you should move −36 to the right by adding 36, not subtracting 36). The other center/radius options are false.
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