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WMA12/01 Oct 2020, Question 4: Circles Meeting Lines, and Tangents

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 9 marks

The question, in short

Given points P(−11, 6) and Q(−3, 12) with PQ a diameter of circle C, find the centre, radius, circle equation and tangent at Q in the form ax + by + c = 0.

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, given that PQ is a diameter.

  1. 1Centre is the midpoint of PQ
  2. 2((−11 + (−3))/2, (6 + 12)/2) = (−7, 9)

Answer(−7, 9)

Part (aii) · 2 marks

Find the radius of circle C from the diameter endpoints P and Q.

  1. 1r = distance from centre (−7, 9) to Q (−3, 12)
  2. 2r = √((−3 + 7)² + (12 − 9)²) = √(16 + 9)
  3. 3r = 5

Answerr = 5

Part (b) · 2 marks

Using the centre and radius, find an equation of circle C.

  1. 1Circle with centre (a, b), radius r: (x − a)² + (y − b)² = r²
  2. 2(x + 7)² + (y − 9)² = 25

Answer(x + 7)² + (y − 9)² = 25

Part (c) · 3 marks

Find the tangent to C at Q, giving it as ax + by + c = 0 with integer coefficients.

  1. 1Gradient of radius to Q = (12 − 9)/(−3 + 7) = 3/4
  2. 2Tangent is perpendicular, so gradient = −4/3
  3. 3y − 12 = −4/3(x + 3)
  4. 43y − 36 = −4x − 12, so 4x + 3y − 24 = 0

Answer4x + 3y − 24 = 0

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Also searched as: WMA12 October 2020 · WMA12/01 · wma12 oct20 · IAS Maths Pure Mathematics 2 October 2020 · question 4.
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