# For f(x, y)=x-y, how do you prove that the equation #f(x, y)= x f(y,x)# represents a hyperbola? find its asymptotes?

##### 1 Answer

Oct 22, 2016

The graph is two lines.

#### Explanation:

Substituting

We'll consider two cases, now:

**Case 1:**

Then we can divide both sides by

Thus, for

**Case 2:**

Then

As this is a tautology,

Taken together, our graph becomes two lines: the line with slope