Cambridge IGCSE · Mathematics - Additional (0606)

Coordinate geometry of the circle: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Coordinate geometry of the circle.

10 questions27 marksFree, no account

Question 1

1 mark

A circle has its centre at the point \((5, 12)\) and passes through the origin \((0, 0)\). Calculate the radius of the circle.

Question 2

1 mark

Determine the points of intersection between the line \(y = 2x\) and the circle \(x^2 + y^2 - 10x = 0\).

Question 3

1 mark

A circle has its centre at the point \((2, -3)\) and passes through the point \((5, 1)\). Find the equation of the circle in the form \(x^2 + y^2 + 2gx + 2fy + c = 0\).

Question 4

1 mark

Find the equation of the circle with centre \((4, -1)\) and radius \(3\).

Question 5

1 mark

The circle \(x^2 + y^2 - 4x + 2y + k = 0\) has a radius of \(3\) units. Find the value of the constant \(k\).

Question 6

2 marks

A circle has the equation \(x^2 + y^2 - 8x = 9\). State the coordinates of its centre and the length of its radius.

Write your answer out first, then check it against the worked solution.

Question 7

5 marks

The line \(y = x + 1\) intersects the circle \(x^2 + y^2 = 13\) at points \(A\) and \(B\). Calculate the length of the chord \(AB\).

Write your answer out first, then check it against the worked solution.

Question 8

6 marks

A circle passes through the points \(P(0, 5)\) and \(Q(0, -1)\). Given that the centre of the circle lies on the line \(y = x\), find the equation of the circle.

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

The equation of a circle is given by \(x^2 + y^2 + 6x - 4y - 12 = 0\).
(a) Show that the point \(P(1, 5)\) lies on the circumference of the circle.
(b) Find the coordinates of the point \(Q\) such that the line segment \(PQ\) forms a diameter of the circle.

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

The points \(A(1, 1)\) and \(B(7, 9)\) are the endpoints of a diameter of circle \(C\).
(a) Find the equation of circle \(C\) in the form \(x^2 + y^2 + gx + fy + c = 0\).
(b) Determine whether the point \(Q(8, 2)\) lies inside, outside, or on the circumference of the circle. Justify your answer.

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, marked as you go.