Thread: help with level curve

I have
x^2 +xy

I want to sketch level curves for it but I'm stuck at simplifying it. I can factor out the x or complete the square but how do I find out what the curve is?

so another form is
(x+½y)^2 - 0.25y^2

so if I let c = 2 for example I'll get

(x+½y)^2 - 0.25y^2 = 2

what do I do now?

If then to plot level curves we choose values of a constant such that .

If , then . Now, graph as a function of in the plane for varying values of