CAIE A-Level Mathematics 1.3.3 Circle Equations

CAIE A-Level Mathematics 1.3.3 Circle Equations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise reading a circle's centre and radius, completing squares in expanded equations and forming circle equations from centres, points, diameters or geometric constraints.

How this is tested

  • read the centre (a, b) and radius r directly from (x − a)² + (y − b)² = r²
  • complete squares in x² + y² + 2gx + 2fy + c = 0 to recover centre and radius
  • use a point, diameter endpoints or centre distance to determine the required radius squared

Question 1

[Maximum number: 5]

A circle has centre (2,6) and radius 10.

Question 1(a)

(a)

State the equation of the circle.

[ 2 ]

Question 1(b)

(b)

The circle passes through the point (8, k).

Find the two possible values of k.

[ 3 ]