# Math Help - help with level curve

1. ## 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?

2. ## Re: help with level curve

If $f(x,y)=x^2+xy$ then to plot level curves we choose values of a constant $c$ such that $f(x,y)=c$.

If $f=c$, then $c=x^2+xy\Rightarrow{y}=\frac{c-x^2}{x}$. Now, graph $y$ as a function of $x$ in the plane for varying values of $c$