Cartesian Equations and Graphs of Circles and Ellipses

This applet investigates Cartesian Equations and Graphs of Circles and Ellipses. Because these are not one-one functions they cannot be described in the usual y = f(x) format, but use equations involving y² and x² instead.

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 or an ellipse 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, C and D to move and change the shape. See how these values relate to the equation and the shape on the screen.
A challenge! - Pressing the "Random" button generates a random circle or ellipse, in yellow. See if you can cover this shape with the white by adjusting the values of A, B, C and D. If you check the box "Circles only" then the random shape will always be a circle. Have fun investigating this topic!