Equation of a Circle (Cambridge International A-Level Mathematics)

Equation of a circle

What is the equation of a circle?

• A circle with centre (a, b) and radius r has the equation

$(x-a)^{2}+(y-b)^{2}=r^{2}$

• You need to be able to find the centre and radius of a circle from its equation

• You need to be able to find the equation of a circle given its centre and radius

Exam Hint

• Remember that the numbers in the brackets have the opposite signs to the coordinates of the centre.
• Don't forget to take the square root of the right-hand side of the equation when finding the radius.

Worked Example