4MA1/2HR Jun 2020, Question 22: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
Find the exact distance AB between the intersection points of the circle x² − x + y² = 10 and the line x − y = −4, giving the answer as √a/2.
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Solution · 6 marks
- 1x − y = −4 gives x = y − 4
- 2Substitute into x² − x + y² = 10: (y − 4)² − (y − 4) + y² = 10
- 3y² − 8y + 16 − y + 4 + y² = 10
- 42y² − 9y + 10 = 0
- 5(2y − 5)(y − 2) = 0
- 6y = 2.5 or y = 2
- 7x = 2.5 − 4 = −1.5 or x = 2 − 4 = −2
- 8so A is (−1.5, 2.5) and B is (−2, 2)
- 9AB = √((−1.5 − (−2))² + (2.5 − 2)²) = √(0.5² + 0.5²)
- 10AB = √0.5 = 1/√2 = √2/2
Answer√2/2 (a = 2)
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