The problem that I have to solve sounds like this:
Sketch the level contours of $f(x,y)$ in a region including all the critical points where $f(x,y)$ = $4x^2y + 4x^2+y^2-2y+1$
I know that the level sets or the set of contours is:
- $L_C = \{ \forall c \in R | f(x,y) = c \}$
I managed to break down the problem into:
- $f(x,y) = 4x^2(y+1) + (y-1)^2 = c \to f(x,y) = (\frac{2x\sqrt{y+1}}{\sqrt{c}}) ^2 + (\frac{y-1}{\sqrt c})^2 = 1$
But from here I am lost..I just don't know how to plot hyperbolae. I would loove to get insight in how to solve this, thanks!!