Lemmara logoLemmaraWorked solution

WMA12/01 Jan 2024, Question 3: The Equation of a Circle

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Circle C has centre A(3, 5) and passes through B(8, −7). Find an equation for C, then find an equation for the horizontal chord MN of length 4√22 lying above the x-axis.

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

Part (a) · 3 marks

Find an equation for the circle with centre A(3, 5) that passes through B(8, −7).

  1. 1r² = (8 − 3)² + (−7 − 5)² = 25 + 144 = 169
  2. 2Centre (3, 5), so (x − 3)² + (y − 5)² = 169

Answer(x − 3)² + (y − 5)² = 169

Part (b) · 3 marks

Points M and N on C form a horizontal chord of length 4√22 above the x-axis; find an equation for the line through M and N.

  1. 1Half of MN is 2√22, and the radius is 13
  2. 2Distance from centre to chord: d² + (2√22)² = 13²
  3. 3d² = 169 − 88 = 81, so d = 9
  4. 4MN is above the x-axis, so y = 5 + 9 = 14

Answery = 14

Stuck on a step? Read the free lesson: The Equation of a Circle

Practise more the equation of a circle questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on the equation of a circle

Also searched as: WMA12 January 2024 · WMA12/01 · wma12 jan24 · IAS Maths Pure Mathematics 2 January 2024 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.