Question

How would I test for symmetry

Example: x^2 + xy + y^2 = 0

Answer 1

multply and divide by (x-y) and will result to you

Answer 2

\[(x-y)(x ^{2}+xy+y ^{2})=x ^{3}-y ^{3}\]

Answer 3

and this divided by (x-y)

Answer 4

\[(x ^{3}-y ^{3})/(x-y)\]

Answer 5

that is the equation for an ellipse with radius zero.
to find symmetry draw a picture ,of
x^2+xy+y^2=c
where you draw a a few values of c

these lines are all symmetric about both x=y, and x=-y