Circle Equations: GCSE Maths Practice | Revision Workshop
Straight-line graphs
Circle Equations
31 self-marking GCSE practice questions on Circle Equations, written specifically for AQA, Pearson, OCR across Higher tier. Instant marking with full worked solutions on every question.
A few of the 31 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 11 markGrade 4-5
A circle has centre the origin, O, and radius 10. Write down the equation of the circle.
Show the worked solution
A circle with centre the origin and radius r has equation x2+y2=r2
What are the common mistakes in Circle Equations?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Mishandles the sign when finding the negative reciprocal for a perpendicular gradient
Took the reciprocal of the radius's gradient but forgot to flip the sign - a perpendicular gradient is the NEGATIVE reciprocal
Gives r^2 as the final answer instead of taking the square root to find r
Wrote down r2=100 itself instead of taking the square root to find r=10
Quick answers about Circle Equations
How many Circle Equations practice questions are there?
There are 31 self-marking GCSE Maths questions on Circle Equations, written for AQA, Pearson, OCR across Higher tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Circle Equations?
No. You can start practising Circle Equations straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
. Here
r=10
, so the equation is
x2+y2=100
.
Question 22 marksGrade 6-7
The point P(−9,12) lies on the circle x2+y2=225, centre the origin O. The radius OP has gradient −1.3333. Work out the gradient of the tangent to the circle at P.
Show the worked solution
The tangent at P is perpendicular to the radius OP, so its gradient is the negative reciprocal of −1.3333: m=−−1.33331=0.75
Question 33 marksGrade 7
Find the exact coordinates of the two intersections of the line y=2x and the circle x2+y2=30.
Question 47 marksGrade 7-8
The line y=3x+p and the circle x2+y2=53 intersect at points A and B. p is a positive integer.
(a) Show that the x-coordinates of A and B satisfy 10x2+6px+p2−53=0.
(b)(i) The coordinates of A are (2, 7). Work out the value of p.
(b)(ii) Work out the coordinates of B, showing your working.
Question 54 marksGrade 8-9
The circle x2+y2=45 has the point (−3,6) on its circumference.
a) Show that the tangent to this circle at the point (−3,6) has a gradient of 21.
b) Find the equation of the tangent at the point (−3,6).
Question 66 marksGrade 8
The diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2).
(a) Write down the equation of the circle.
(b)(i) Work out the gradient of the radius to the point (4, 2).
(b)(ii) Hence show that the tangent to the circle at the point (4, 2) has gradient −2.
(b)(iii) Find the equation of the tangent to the circle at the point (4, 2).
Misapplies the negative-reciprocal rule when finding the gradient of a perpendicular line
Used the RADIUS's gradient (-2) itself as the tangent's gradient, instead of the negative reciprocal - a tangent to a circle is always PERPENDICULAR to the radius at that point.