WMA12/01 Jun 2025, Question 2: The Equation of a Circle
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks
The question, in short
Find a circle equation from a diameter with endpoints (−2, 5) and (4, 15), then locate the closest point to the x-axis.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 5 marks
Work out the centre and radius from the diameter endpoints, then write the circle equation.
- 1Centre = midpoint = ((−2 + 4)/2, (5 + 15)/2) = (1, 10)
- 2Diameter² = (4 − (−2))² + (15 − 5)² = 36 + 100 = 136
- 3Radius² = 136 ÷ 4 = 34
- 4Equation: (x − 1)² + (y − 10)² = 34
Answer(x − 1)² + (y − 10)² = 34
Part (b) · 2 marks
Use the circle equation to find exact coordinates of the point closest to the x-axis.
- 1The nearest point to the x-axis is directly below the centre (1, 10)
- 2Its y-coordinate is 10 − √34 (radius √34 ≈ 5.83, so it is still above the axis)
- 3Point: (1, 10 − √34)
Answer(1, 10 − √34)
Stuck on a step? Read the free lesson: The Equation of a Circle
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