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WMA12/01 Jun 2021, Question 6: Circles with Unknowns and Axes

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Circle equation x² − 6x + y² + 8y + k = 0 with k positive and x-axis tangent; find k, then exact area of triangle RST where circle meets the axes.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Find the value of k given that the x-axis is tangent to the circle.

  1. 1(x − 3)² + (y + 4)² = 25 − k
  2. 2Centre (3, −4); the x-axis is a tangent so the radius is 4
  3. 325 − k = 16
  4. 4k = 9

Answerk = 9

Part (b) · 4 marks

Find the exact area of triangle RST formed by the points where the circle meets the coordinate axes.

  1. 1The circle touches the x-axis at (3, 0)
  2. 2On the y-axis, x = 0: y² + 8y + 9 = 0, so y = −4 ± √7
  3. 3Distance between the y-axis points = 2√7; height of the triangle = 3
  4. 4Area = ½ × 2√7 × 3 = 3√7

Answer3√7

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Also searched as: WMA12 June 2021 · WMA12/01 · wma12 jun21 · IAS Maths Pure Mathematics 2 June 2021 · question 6.
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