Equation of a circleEdexcel International A Level Maths: Mind map

Equation

Reading it

Building it

Circles

(x-a)² + (y-b)² = r²

centre (a, b)radius r

Expanded form

Points and lines

Exam tips

Exam questions on Equation of a circle

A circle has equation $(x-3)^2+(y+2)^2=25$ .
Determine whether the point $(6,2)$ lies inside, outside or on the circle.2 marks
A circle has centre $(-4,1)$ and passes through the point $(-2,4)$ .
Find the coordinates of the points where the circle meets the line $y=1$ .2 marks
A circle $C$ has equation $x^2+y^2-10x+4y+13=0$ .
Find the coordinates of the centre of $C$ and the radius of $C$ .3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).