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WMA12/01 Jun 2019, Question 2: Circles Meeting Lines, and Tangents

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

The question, in short

For the circle with equation x² + y² + 4x − 10y − 21 = 0, determine its centre and exact radius, then use point P(5, 4) on the circle to find the tangent line there in y = mx + c form.

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

Part (a) · 3 marks

Give the centre coordinates of the circle and the exact radius value.

  1. 1(x + 2)² − 4 + (y − 5)² − 25 − 21 = 0
  2. 2(x + 2)² + (y − 5)² = 50
  3. 3Centre (−2, 5)
  4. 4Radius = √50 = 5√2

AnswerCentre (−2, 5); radius √50 = 5√2

Part (b) · 4 marks

Using P(5, 4) on the circle, derive the tangent line's equation as y = mx + c, stating m and c.

  1. 1Gradient of radius CP = (5 − 4)/(−2 − 5) = −1/7
  2. 2Tangent is perpendicular to radius, so gradient = 7
  3. 3y − 4 = 7(x − 5)
  4. 4y = 7x − 31

Answery = 7x − 31

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Also searched as: WMA12 June 2019 · WMA12/01 · wma12 jun19 · IAS Maths Pure Mathematics 2 June 2019 · question 2.
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