Geometry and TrigonometryHardRadius by completing two squares
Geometry and Trigonometry practice question
In the xy-plane, the equation x² + y² + 8x − 2y + 8 = 0 describes a circle. What is the radius of the circle?
Answer: 3
Complete the squares: (x + 4)² + (y − 1)² = 16 + 1 − 8 = 9, so the radius is 3.
Common wrong answers
- If you answered 4
- 4 is the center's x-offset magnitude, not the radius.
- If you answered 8
- 8 is the constant moved across; combine it with 16 and 1 first.
- If you answered 9
- 9 is the radius squared.
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