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 20051216 11:41:27 