Question

Find the locus of points (x,y) for which x^3 + y^3 + 3xy = 1.

Answer 1

The locus of point (x,y)
is x^3+y^2+3xy-1 = 0
as it satisfies every condition for (x,y).

Answer 2

[tex]x^{3} + y^{3} -1 = -3xy [/tex]
Therefore,
$x + y - 1 = 0$
$x+y = 1$
This means that the locus is a straight line.