For function

Find all stationary points and describe their nature.

So this is what I did, first I took the two partial derivatives.

Allow the partial derivatives to equal zero to equate the critical points.

For

I divided both sides by y (not sure if this was a mistake or not), and for

I divided both sides by x.

This left me with:

and

From here, do I allow the two equations to equal each other and equate from there, or is that just going to get me into a muddle?

I can't seem to work out a simple method to finding values that satisfy both equations aside from guessing (embarrasing I know).

Thanks in advance,