Equation of a Circle

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Play around with the sliders to change the circle

The equation for a circle, as written above, is \[(x - a)^2 + (y - b)^2 = r^2\] where: \(x\) and \(y\) are cartesian coordinates, \((a,b)\) is the centre of the circle, and \(r\) is the radius. By moving the sliders, you can change these variables, and see instantly how they reflect on what the circle looks like!

If you increase \(a\), it will move the centre (and so the whole circle) to the right. Likewise if you decrease \(a\) it will move to the left. Increasing or decreasing \(b\) will move the circle up or down respectively. As \(r\) is the radius, the circle grows or shrinks as you play with its value.

Challenge yourself

Why not pick some values for \(a\), \(b\) and \(r\), then try sketching the circle on paper? You can check your sketch by choosing matching values above.


You can zoom in and out using the + and - buttons in the bottom right corner. Note that there is a limit to how far you can zoom in either direction.


If you find any problems or have ideas for improvements, contact by Twitter: @NextLevelMaths.