# 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 `y`² and `x`² instead.

###### Author and programmer: Ron Barrow

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

TweetInstructions below See also: Parametric Equations of Circles and Ellipses

## 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!