Lemmara logoLemmaraWorked solution

0606/21 Oct/Nov 2025, Question 5: Circles Meeting Lines, and Tangents

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given a circle centred at (4, 2) passing through (−2, 0), determine its equation and the exact coordinates where it crosses the y-axis.

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

Part (a) · 2 marks

Work out the equation of the circle with centre (4, 2) that goes through (−2, 0).

  1. 1r² = (4 − (−2))² + (2 − 0)² = 36 + 4 = 40
  2. 2(x − 4)² + (y − 2)² = 40

Answer(x − 4)² + (y − 2)² = 40

Part (b) · 3 marks

Using exact values, work out the coordinates of the two points where this circle crosses the y-axis.

  1. 1On the y-axis x = 0: 16 + (y − 2)² = 40
  2. 2(y − 2)² = 24
  3. 3y = 2 ± √24 = 2 ± 2√6
  4. 4Points (0, 2 + 2√6) and (0, 2 − 2√6)

Answer(0, 2 + √24) and (0, 2 − √24)

Stuck on a step? Read the free lesson: Circles Meeting Lines, and Tangents

Practise more circles meeting lines, and tangents questions

Real 0606 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 circles meeting lines, and tangents

Also searched as: 0606/21/O/N/25 · 0606_w25_qp_21 · 0606 w25 21 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.