4MA1/2H Nov 2021, Question 19: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
Solve the line x − y = 3 with the curve 3x² − y² + xy = 9 to find intersection points P and Q, then find the midpoint of PQ, showing algebraic working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1From L: y = x − 3; substitute: 3x² − (x − 3)² + x(x − 3) = 9
- 23x² + 3x − 18 = 0, so x² + x − 6 = 0
- 3(x + 3)(x − 2) = 0: P(−3, −6) and Q(2, −1)
- 4Midpoint = ((−3 + 2)/2, (−6 − 1)/2) = (−1/2, −7/2)
Answer(−1/2, −7/2)
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