A question related to Derivative Rules.

Hey everyone. :)

I'm currently trying to solve a problem from my textbook that was assigned for homework. It reads;

"Let P(a, b) be a point on the curve sqroot(x) + sqroot(y) = 1. Show that the slope of a tangent at P is -sqroot(b/a)."

Using Graphmatica, (1/x^2)+(1/y^2)=1 shows four asymptotes, one in each quadrant, all approaching 1 or (-1) (depending on the positive/negative side of the y axis).

How abouts do I solve this?

Any insight would be helpful. :)