4MA1/2H Jan 2020, Question 22: Simultaneous Equations with a Curve
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Solve the line y = x + 2 with the circle x² + y² − 2y = 24 to find the coordinates of the two intersection points A and B, showing algebraic working.
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Solution · 5 marks
- 1Substitute y = x + 2: x² + (x + 2)² − 2(x + 2) = 24
- 2Expand: 2x² + 2x − 24 = 0, so x² + x − 12 = 0
- 3(x + 4)(x − 3) = 0, so x = −4 or x = 3
- 4y = x + 2 gives (−4, −2) and (3, 5)
Answer(−4, −2) (3, 5)
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