2x^2 + 2y^2 + x + y = 0
Show complete working out.
Your question is not at all clear. You could "sketch" the graph by calculating several points: if x= 0, so y= 0 or -1/2. and are points on the graph. Taking y= 0, we get, in exactly the same way, which we had before, . Get enough points that way and you can sketch the graph.
But I suspect that you are intended to complete the square to see what kind of figure this is:
If you divide through by 2 you get . Presumably you know that . Comparing that to , they match if a= 1/4 and we can make this a "perfect square by adding . Doing that for both x and y, or . What kind of figure is that?