Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top


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

How do I go about doing this?

share|cite|improve this question
up vote 0 down vote accepted

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?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.