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WMA12/01 Jun 2023, Question 3: Circles Meeting Lines, and Tangents

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

The question, in short

Circle C has centre (2, 5) and passes through P(8, −3). Find its radius, its equation, and the tangent at P in the form ax + by + c = 0 with integer coefficients.

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Part (ai) · 2 marks

Find the radius of circle C using the centre (2, 5) and point P(8, −3).

  1. 1r = √((8 − 2)² + (−3 − 5)²)
  2. 2= √(36 + 64) = √100
  3. 3r = 10

Answerr = 10

Part (aii) · 1 mark

Write down an equation for circle C with centre (2, 5) and the radius found.

  1. 1Centre (2, 5), radius 10
  2. 2(x − 2)² + (y − 5)² = 10² = 100

Answer(x − 2)² + (y − 5)² = 100

Part (b) · 4 marks

Find the tangent to C at P(8, −3), giving it as ax + by + c = 0 with integers a, b, c.

  1. 1Gradient of radius from (2, 5) to (8, −3) = (−3 − 5)/(8 − 2) = −4/3
  2. 2Tangent is perpendicular to the radius: gradient = 3/4
  3. 3y + 3 = (3/4)(x − 8)
  4. 44y + 12 = 3x − 24
  5. 53x − 4y − 36 = 0

Answer3x − 4y − 36 = 0

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Also searched as: WMA12 June 2023 · WMA12/01 · wma12 jun23 · IAS Maths Pure Mathematics 2 June 2023 · question 3.
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