A ladder (shown as segment AB) is leaning against the wall and sliding down.[br]Drag point A to slide the ladder. Try to express the contour of its trace by using an algebraic expression.

By using GeoGebra's [b]Envelope[/b] command you can find the algebraic object. Also you can see 4 copies of the same curve, which as a whole, is called [i]astroid[/i]. Red lines are the tangents of the astroid.[br][list=1][*]Find the 6th order polynomial manually. Compare your result with [url=http://en.wikipedia.org/wiki/Astroid]http://en.wikipedia.org/wiki/Astroid[/url].[/*][*]Also compare your result with [url=http://en.wikipedia.org/wiki/Envelope_(mathematics)#Example_4]http://en.wikipedia.org/wiki/Envelope_(mathematics)#Example_4[/url].[br][/*][/list]