This applet investigates Cartesian Equations and Graphs of Circles and Ellipses

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

Instructions below See also:   Parametric Equations of Circles and Ellipses

[Applet - Ellipse1L - Circles and Ellipses]

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!