How Do You Sketch Level Curves for T(x,y) = (2x+y)/(x^2 -y^2)?

[curious_iza]

Hi this is the question that I am unsure about...

Find and then sketch the level curves of the scalar field T(x,y) = (2x+y)/(x^2 -y^2) for;
T = -1
T = -0.5
T = 0
T = 0.5
T = 1

I am unsure about these answers which I got by subbing each of the values into T(x,y)

1) T = -1

After gathering x and y values on one side of the equation and completeing the square I got;

(x + 1)^2 -(y - 0.5)^2 = 3/4 ...

I am unsure about what kind of graph this is because I know that a hyperbola should be equal to 1 and this isn't.

T = -0.5

For this one I got (x + 2)^2 -(y - (0.5))^2 = (15/4)

T = 0
Finally one I could do :)

y = 2x

T=0.5
(x - 2) ^2 - (y +1)^2 = 3

T = 1
(x - 1)^2 - (y - 1/2)^2 = 3/4

I am pretty sure that I got the equations correct but I would appreciate if someone could help me with;

a) Explaining how I draw this since it is not in the form of a hyperbola ie not = 1.

b) What these mean?

 

[CompuChip]

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