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WMA12/01 Jan 2020, Question 6: Chords and Tangent Geometry

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 8 marks

The question, in short

For circle C with equation x² + y² + 6x − 4y − 14 = 0, find its centre and exact radius, then use horizontal lines to find tangent k values and a chord value p.

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

Part (ai) · 2 marks

Find the coordinates of the centre of circle C.

  1. 1(x + 3)² − 9 + (y − 2)² − 4 − 14 = 0
  2. 2(x + 3)² + (y − 2)² = 27
  3. 3Centre (−3, 2)

Answer(−3, 2)

Part (aii) · 1 mark

Find the exact radius of circle C.

  1. 1(x + 3)² + (y − 2)² = 27
  2. 2r = √27 = 3√3

Answer3√3

Part (b) · 2 marks

Given y = k is a tangent to C, find the possible values of k.

  1. 1A horizontal tangent touches the top or bottom of the circle
  2. 2k = 2 ± r
  3. 3k = 2 + 3√3 or k = 2 − 3√3

Answerk = 2 + 3√3 or k = 2 − 3√3

Part (c) · 3 marks

Given y = p (p negative) is a chord of length 4 units, find p.

  1. 1Half the chord is 2, so the distance h from the centre to the chord satisfies h² = 27 − 2²
  2. 2h² = 23, h = √23
  3. 3p = 2 ± √23; p is negative
  4. 4p = 2 − √23

Answerp = 2 − √23

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Also searched as: WMA12 January 2020 · WMA12/01 · wma12 jan20 · IAS Maths Pure Mathematics 2 January 2020 · question 6.
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