The curve defined by the relation x^3+y^3=3xy intersects itself at the origin and forms a loop. Find the area enclosed by the loop.

(In reply to A solution by goFish)

Clearly (0,0) and (1.5,1.5) are points on this curve, but the problem asks for the AREA enclosed by the loop.

The curve is symmetrical around the line y=x

It may help to do a transformation that rotates the x and y axes 45 degrees with a subsequent change in the equation.   But I'll have to look up how to do that again.

Or, polar coordinates (as someone else mentioned)

Posted by Larry on 2005-12-16 11:41:27