0606/22 Feb/Mar 2026, Question 8: Circles Meeting Lines, and Tangents
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 8 marks
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The question, in short
Circle centre (−2, 0) radius 5 and line y = 2x + k that misses the circle; find all possible values of k.
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Solution · 8 marks
- 1Circle: (x + 2)² + y² = 25
- 2Substitute y = 2x + k: (x + 2)² + (2x + k)² = 25
- 35x² + 4(k + 1)x + k² − 21 = 0
- 4No intersection: 16(k + 1)² − 20(k² − 21) < 0
- 5−4k² + 32k + 436 < 0, i.e. k² − 8k − 109 > 0
- 6k = (8 ± √(64 + 436))/2 = 4 ± 5√5
- 7k < 4 − 5√5 or k > 4 + 5√5
Answerk < 4 − 5√5, k > 4 + 5√5 (or k < −7.18, k > 15.2)
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