AQA GCSE Maths
Topic questions Pure mathematics Equation of a circle
16 questions · 58 marks · about 1 hour
Also involves Surds
Write down the equation of the circle.
Work out the equation of the tangent. Give your answer in the form y = mx + c
A circle has centre (0, 0) and circumference 36 π
Work out the equation of the circle.
Point J has coordinates (15, 0) and point K has coordinates (30, – 5)
Work out the equation of the straight line through J and K.
A circle has centre O and passes through (0, 6)
Write down the equation of the circle.
Also involves Parallel and perpendicular lines
(4, 8) is a point on a circle, centre O. The tangent at (4, 8) intersects the x-axis at P.
Work out the x-coordinate of P.
A circle has centre (0, 0) and passes through (0, 11)
Write down the equation of the circle.
Which of these is the equation of a circle? Circle your answer.
Also involves Surds
The equation of a circle is x2 + y2 = 11 Work out the length of the diameter. Circle your answer.
The equation of a circle is x 2 + y 2 = 9 25 Work out the length of the diameter. Circle your answer.
3 6 9 18
Also involves Coordinate geometry · Pythagoras' theorem
P (4, 8) is a point on a circle, centre O. The tangent at P intersects the axes at points A and B.
Show that the gradient of the tangent is – 
Work out the length AB.
You must show your working.
Also involves Ratio
In this question, all lengths are in centimetres. A is a point on a circle, centre O. B is a point on a different circle, centre O.
The equation of the larger circle is x2 + y2 = 144 radius of smaller circle: radius of larger circle = 4: 5
Work out the size of angle A O B.
Also involves Quadratic equations
The line y = 3x + p and the circle x2 + y2 = 53 intersect at points A and B. p is a positive integer.
Show that the x-coordinates of points A and B satisfy the equation
The coordinates of A are (2, 7) Work out the coordinates of B. You must show your working.
A circle, centre O, passes through (5, 0).
What is the equation of the circle? Circle your answer.
Also involves Pythagoras' theorem
P is a point on the circle with equation x2 + y2 = 80 P has x-coordinate 4 and is below the x-axis.
Work out the equation of the tangent to the circle at P.
Also involves Surds · Coordinate geometry · Pythagoras' theorem
A, B and C are points on the circle x2 + y2 = 36 as shown. A is on the y-axis. B is on the x-axis. M is the midpoint of AB. C O M is a straight line.
Show that the coordinates of A are (0, 6)
Work out the coordinates of B.
Show that the equation of the straight line passing through C, O and M is y = x
Work out the coordinates of C. Give your answers in surd form.
Work out the diameter of the circle x2 + y2 = 64 Circle your answer.
8 16 32 128
Also involves Parallel and perpendicular lines · Gradient and intercept
P (–1, 4) is a point on a circle, centre O
Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c
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