Thread: Level Curves question

I have a question asking me to describe the level curves for the following functions f(x,y) = x^2 + 2y^2 - 3x= 0

and

f(x,y) = -6

How do I go about doing this, for the second case, would the level curve be just a line or an empty set?

Originally Posted by Penguin91

I have a question asking me to describe the level curves for the following functions f(x,y) = x^2 + 2y^2 - 3x= 0

and

f(x,y) = -6

How do I go about doing this, for the second case, would the level curve be just a line or an empty set?

The level curves are the sets where the functions values are constant.


So for the first one set



Now complete the square on the x terms to get







This is a familiy of ellipses.

For the 2nd one think of the definition. Where is the function constant

Thanks for your reply, that made more sense!