Geometry and TrigonometryVery hardCentre and radius from the general form
Geometry and Trigonometry practice question
In the xy-plane, the circle x² + y² − 6x + 4y − 12 = 0 has centre (h, k) and radius r. What is the value of h + k + r?
Answer: 6
Complete the squares: (x − 3)² + (y + 2)² = 12 + 9 + 4 = 25. So h = 3, k = −2, r = 5, and h + k + r = 6.
Common wrong answers
- If you answered 10
- 10 takes k = +2 from the sign of 4y without flipping it.
- If you answered 26
- 26 uses r² = 25 instead of r = 5.
- If you answered 4.46
- 4.46 uses r = √12, forgetting to add the completed-square constants.
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