IGCSE · Additional Mathematics 0606 · Geometry & trigonometry

Coordinate geometry of the circle: IGCSE Additional Mathematics questions with answers

Free Coordinate geometry of the circle questions for IGCSE Additional Mathematics (0606), part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.

Generate a full Coordinate Geometry of the Circle worksheet →All Geometry & trigonometry questions

Coordinate geometry of the circle practice questions

Question 1Structured · 5 marksA* challenge

A circle has centre C(3, 1) and passes through the point P(6, 4).

(a)

Find the equation of the circle.

[2]
(b)

Find the equation of the tangent to the circle at P.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)(x − 3)2 + (y − 1)2 = 25
radius 5 B1
(x − 3)2 + (y − 1)2 = 25 B1
2
(b)tangent
gradient CP = 1 B1
tangent gradient −1 M1
y − 4 = −1(x − 6) A1
3
Question 2Structured · 3 marks

A circle has equation x2 + y2 − 8x − 4y + 4 = 0.

Find the centre and the radius of the circle.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
centre (4, 2); radius 4
completing the square M1
centre (4, 2) A1
radius 4 A1
3
Question 3Structured · 2 marks

State what is meant by the term equation of a circle.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(x − a)2 + (y − b)2 = r2, where (a, b) is the centre and r is the radius
(x − a)2 + (y − b)2 = r2, where (a, b) is the centre and r is the radius B2
2
Question 4Structured · 5 marksA* challenge

A circle has centre C(1, 3) and passes through the point P(5, 7).

(a)

Find the equation of the circle.

[2]
(b)

Find the equation of the tangent to the circle at P.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)(x − 1)2 + (y − 3)2 = 25
radius 5 B1
(x − 1)2 + (y − 3)2 = 25 B1
2
(b)tangent
gradient CP = 1 B1
tangent gradient −1 M1
y − 7 = −1(x − 5) A1
3
Question 5Structured · 3 marks

A circle has equation x2 + y2 + 2x + 2y − 7 = 0.

Find the centre and the radius of the circle.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
centre (−1, −1); radius 3
completing the square M1
centre (−1, −1) A1
radius 3 A1
3
Question 6Structured · 5 marksA* challenge

A circle has centre C(3, 2) and passes through the point P(6, 6).

(a)

Find the equation of the circle.

[2]
(b)

Find the equation of the tangent to the circle at P.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)(x − 3)2 + (y − 2)2 = 25
radius 5 B1
(x − 3)2 + (y − 2)2 = 25 B1
2
(b)tangent
gradient CP = 43 B1
tangent gradient −34 M1
y − 6 = −34(x − 6) A1
3

More Geometry & trigonometry questions

Straight-line graphsCircular measureTrigonometry

Want a mentor, not just a paper?

Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

Meet Riyaz →

Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in