Geometry and TrigonometryVery hardCentre from an expanded equation
Geometry and Trigonometry practice question
A circle in the xy-plane has the equation x² + y² + 8x − 6y = 0. What are the coordinates of its centre?
- A. (−4, 3)Correct
- B. (4, −3)
- C. (8, −6)
- D. (−8, 6)
Answer: A. (−4, 3)
Complete the square: (x + 4)² − 16 + (y − 3)² − 9 = 0, so (x + 4)² + (y − 3)² = 25. Centre (−4, 3), radius 5.
Why the other answers are wrong
- B. (4, −3)
- (4, −3) has the signs flipped; (x + 4)² is centred at x = −4.
- C. (8, −6)
- (8, −6) reads the coefficients as coordinates without halving or flipping.
- D. (−8, 6)
- (−8, 6) flips the signs but forgets to halve.
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