Finding Level Curves of f(x,y)=xy

[ozgurakkas]

Question as follows

f(x,y)=xy , find the level curves for c= +-1,+-2,+-3,+-4,+-5

My first attempt was to set f(x,y)=c

c=xy and y=1/x C and this is an hyperbolic function. Is that right?

I am also confused what values x can get. I know it is restricted and x>0.
Can x get the same value as C ?

 

[HallsofIvy]

Question as follows

f(x,y)=xy , find the level curves for c= +-1,+-2,+-3,+-4,+-5

My first attempt was to set f(x,y)=c

c=xy and y=1/x C and this is an hyperbolic function. Is that right?

I am also confused what values x can get. I know it is restricted and x>0.
Can x get the same value as C ?

Why is it restricted to x> 0? Unless something else is said, y= C/x is only restricted to x not 0. Other than that, x can have any positive or negative value whatever C is.

 

[ozgurakkas]

Question does not say it is restricted. I said it because x is in the denumerator. if it is 0 then it is undefined.

 

[HallsofIvy]

Yes. But not being 0 does not mean it must be positive! x can be any positive or negative number.