Surface intersection equation

Question

I am required to find the vector function of a curve which is formed when these two surfaces intersect. A hint would be more than enough.

Answer 1

Hint: we get $$z=\frac{1}{xy}$$ and we Substitute $$y=tx$$ then we get $$x^2(1+t^2)-\frac{1}{tx^2}=1$$ multiplying by $x^2$ we get $$x^4(1+t^2)-\frac{1}{t}=x^2$$ This can be solved for $x=x(t)$