# Thread: scalar field question

1. ## scalar field question

hey people, i have a question asking me to sketch the level curves of this scalar field:

T(x,y) = (2x-y)/(x^2+y^2), for T = -1,-.5,0,.5 and 1.

The theory we were taught was to let T equal a constant and then rearrange the equation to find y in terms of x, but you cannot simply rearrange this equation like that. I know i must have done something like this before, it seems pretty familiar, but it's bugging me :P can someone lend a hand?

2. Originally Posted by ben08
hey people, i have a question asking me to sketch the level curves of this scalar field:

T(x,y) = (2x-y)/(x^2+y^2), for T = -1,-.5,0,.5 and 1.

The theory we were taught was to let T equal a constant and then rearrange the equation to find y in terms of x, but you cannot simply rearrange this equation like that. I know i must have done something like this before, it seems pretty familiar, but it's bugging me :P can someone lend a hand?

If T=1

we get...

$1=\frac{2x-y}{x^2+y^2} \iff x^2+y^2=2x-y \iff x^2-2x+y^2+y=0$
if you complete the square we will get an equation of a circle.

$x^2-2x+1+y^2+y+\frac{1}{4}=1+\frac{1}{4} \iff (x-1)^2+(y+\frac{1}{2})^2=\frac{5}{4}$

I hope this helps.

Good luck

3. Originally Posted by ben08
hey people, i have a question asking me to sketch the level curves of this scalar field:

T(x,y) = (2x-y)/(x^2+y^2), for T = -1,-.5,0,.5 and 1.

The theory we were taught was to let T equal a constant and then rearrange the equation to find y in terms of x, but you cannot simply rearrange this equation like that. I know i must have done something like this before, it seems pretty familiar, but it's bugging me :P can someone lend a hand?
I'll do one of them - it should be very obvious how to do the others.

$1 = \frac{2x-y}{x^2 + y^2} \Rightarrow x^2 + y^2 = 2x - y \Rightarrow x^2 - 2x + y^2 + y = 0$.

Complete the square in x-terms and y-terms and re-arrange to get the standard form of a circle.

4. ## thanks

thanks for the help, i knew it was something simple that i hadn't used in a while

### how to sketch scalar fields

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