Question 979289
Try completing the squares (if necessary).


{{{y^2+y-x^2-2x=0}}}
{{{y^2+y+(1/2)^2-(x^2+2x+(1/2)^2)=(1/2)^2-(1/2)^2}}}
{{{(y+1/2)^2-(x+1/2)^2=0}}}


Degenerate Hyperbola.