0606/23 Oct/Nov 2025, Question 6: The Perpendicular Bisector
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 9 marks
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The question, in short
Find where the line y = 3x + 4 intersects the curve y = 2x² + 8x + 1 at points A and B, then find the perpendicular bisector of AB in the form ax + by + c = 0 with integer coefficients.
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Solution · 9 marks
- 13x + 4 = 2x² + 8x + 1 gives 2x² + 5x − 3 = 0
- 2(2x − 1)(x + 3) = 0: A and B are (1/2, 11/2) and (−3, −5)
- 3Midpoint = (−1.25, 0.25)
- 4Gradient of AB = 3, so perpendicular gradient = −1/3
- 5y − 1/4 = −(1/3)(x + 5/4)
- 6Multiply by 12: 12y − 3 = −4x − 5
- 72x + 6y + 1 = 0
Answer2x + 6y + 1 = 0
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Also searched as: 0606/23/O/N/25 · 0606_w25_qp_23 · 0606 w25 23 · question 6.
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