Cartesian Equations of Circles

This applet investigates Graphs of Circles and two forms of their Cartesian Equations. A circle can be described by the coordinates of its centre and its radius. This gives an equation with brackets (parentheses). The other form is obtained by "completing the square" and rearranging.

Author and programmer: Ron Barrow

UK Years 12-13, KS5, GCE AS Level Core Mathematics, C1, C2, Coordinate Geometry

   
           

Instructions below    See also:   Parametric Equations of Circles and Ellipses

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How to Use this Applet

A circle can be described by a pair of parametric equations, or by a single Cartesian Equation, which directly connects the x- and y- values on a Cartesian coordinate graph. This applet is about Cartesian equations.
You can vary A, B, and R to move and change the shape. See how these values relate to the equation and the circle on the screen.

A challenge! - Pressing the "Random" button generates a random circle. See if you can cover the equation of this circle by adjusting the values of A, B, and R until the circles coincide.
Have fun investigating this topic!