0606/23 Oct/Nov 2025, Question 11: Two Circles
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 5 marks
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The question, in short
Given a circle x² + y² − 25 = 0 and a second circle of equal radius with positive centre coordinates, whose common chord AB has length 6 and is parallel to y = −x, find the second circle's equation as x² + y² + ax + by + c = 0.
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Solution · 5 marks
- 1Both circles have radius 5
- 2The line of centres is perpendicular to AB, so the second centre lies on y = x, at (k, k) with k > 0
- 3Half of AB = 3, so the distance from O to AB = √(5² − 3²) = 4 and the distance between the centres = 8
- 4k√2 = 8, so k = 4√2: centre (4√2, 4√2)
- 5(x − 4√2)² + (y − 4√2)² = 25
- 6x² + y² − 8√2x − 8√2y + 39 = 0
Answerx² + y² − 8√2x − 8√2y + 39 = 0
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Also searched as: 0606/23/O/N/25 · 0606_w25_qp_23 · 0606 w25 23 · question 11.
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