captain pi your are so close,
the correct answer is
locus of w os a circle, radious 2/3(SQRT)5, Center (-4/3,2/3)
this is your mistake:
it should be:
3x² + 8x + 3y² - 4y = 0
well done though, thanks for the explination.
Wow... that is... so..... nerdy.... I think that reaches...