# Thread: Help with level curve!

1. ## Help with level curve!

Hi.

I want to draw the level curve for the following function.

f(x,y) = [x-y^2]/[x^2+y]

so if i set c = [x-y^2]/[x^2+y], how can I solve for y? Basically i need y in terms of c and x so I can draw them do i not?

2. ## Re: Help with level curve!

Originally Posted by Kuma
Hi.I want to draw the level curve for the following function. f(x,y) = [x-y^2]/[x^2+y]
I don't know the context of the problem and perhaps you only need to draw the zero level curve. In that case

$\frac{x-y^2}{x^2+y}=0\Leftrightarrow (x-y^2=0)\;\wedge (x^2+y\neq 0)$

That is, the parabola $x=y^2$ excluding the points $(0,0),\;(1,-1)$ .

3. ## Re: Help with level curve!

Yes at the point 0 I will get a parabola, but I want to draw the level curves for more than 1 point. Suppose c=-2 and c=2, what can i do then?

4. ## Re: Help with level curve!

Originally Posted by Kuma
Yes at the point 0 I will get a parabola, but I want to draw the level curves for more than 1 point. Suppose c=-2 and c=2, what can i do then?
Is it out of curiosity? You can use the Newton-Cramer method, but I guess you haven't covered it.

5. ## Re: Help with level curve!

Originally Posted by FernandoRevilla
Is it out of curiosity? You can use the Newton-Cramer method, but I guess you haven't covered it.
Well it is a question and it asks me to draw more than one level curve, and I would also like to know how to do them because this is a weak point of mine. So basically the only other way to draw these is using the newton cramer method?

6. ## Re: Help with level curve!

Originally Posted by Kuma
Hi.

I want to draw the level curve for the following function.

f(x,y) = [x-y^2]/[x^2+y]

so if i set c = [x-y^2]/[x^2+y], how can I solve for y? Basically i need y in terms of c and x so I can draw them do i not?
$cx^2 + cy = x - y^2 \Rightarrow cx^2 + x + y^2 + cy = 0$.

Complete the square in x and y terms and consider what the resulting relation defines for suitable values of c.

7. ## Re: Help with level curve!

I feel stupid!. A simple conic!