# Finding level curves of this function

$$x^{2}+2ky+y^{2}=u(x,y,k)$$

If $k$ is made constant, what are the level curves of $u$?

How do I go about doing this?

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You want to find the set of points $(x,y)$ that satisfy the equation $$x^2+2ky + y^2 = u$$ for $k$ and $u$ constants. First, you can complete the square to get $$x^2 + (y+k)^2 = u+k^2.$$ What does the set of points satisfying this equation look like?