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WMA12/01 Oct 2019, Question 6: Chords and Tangent Geometry

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

The question, in short

For circle C with centre N(4, −1) and tangent line y = (1/2)x meeting it at P, find the line PN and the circle's equation.

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

Part (a) · 2 marks

Find the equation of line PN, giving it in the form y = mx + c.

  1. 1PN is a radius, so it is perpendicular to the tangent of gradient 1/2
  2. 2Gradient of PN = −2
  3. 3Through N(4, −1): y + 1 = −2(x − 4)
  4. 4y = −2x + 7

Answery = −2x + 7

Part (b) · 5 marks

Find the equation of circle C.

  1. 1P is where y = (1/2)x meets y = −2x + 7: (1/2)x = −2x + 7
  2. 2x = 14/5, y = 7/5, so P = (14/5, 7/5)
  3. 3r² = (4 − 14/5)² + (−1 − 7/5)² = 36/25 + 144/25 = 36/5
  4. 4C: (x − 4)² + (y + 1)² = 36/5

Answer(x − 4)² + (y + 1)² = 36/5

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Also searched as: WMA12 October 2019 · WMA12/01 · wma12 oct19 · IAS Maths Pure Mathematics 2 October 2019 · question 6.
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