Instead of using a single equation to generate a curve, two parametric equations are used.
Here the letter t denotes the parameter, and the x- and y- coordinates are calculated from the formulas:

You can vary the values of A, B, C and D using the buttons at the bottom.
By varying A and C you can create a series of circles and ellipses.
Varying B and D complicates the situation by drawing the strikingly beautiful Lissajou Figures.
You can hide the axes by unchecking the box marked "Show Axes". You can also generate a random figure by clicking the "Random" button with your mouse.
Play around - enjoy yourself!