Introduction

Change the values of $$a$$, $$b$$ and $$r$$ to see different circles. Write down the centre and radius for each circle. How can you predict the centre and radius from the equation of the circle?

Use the checkbox to show a triangle on the circle. Write down expressions in terms of $$a$$, $$b$$ and $$r$$ for the length of each side. How does this explain the equation of the circle?

Created with GeoGebra

Simple form

Finding the centre and radius of a circle from its equation

Give your answers as exact whole numbers.

The centre of the circle has coordinates ( , ) and the radius of the circle is



Click the New button to generate another question

Expanded form

Finding the centre and radius of a circle in the form $$ x^{2} + fx + y^{2} + gy + c = 0$$

Read the question and then use the Next button to advance through the solution

 
 

Click the New button to generate another example

Expanded form

Finding the centre and radius of a circle in the form $$ x^{2} + fx + y^{2} + gy + c = 0$$

Use a pen and paper for working as appropriate.
Give your answers as exact whole numbers or as fractions in their lowest terms in the form p/q.

The centre of the circle has coordinates ( , ) and the radius of the circle is



Click the New button to generate another question