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A Self Intersecting Curve (Posted on 2005-12-16) Difficulty: 5 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 4.5000 (2 votes)

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re: A solution; Not quite | Comment 2 of 9 |
(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

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