1. The problem statement, all variables and given/known data Is there anything special about the tangents to the curves xy=1 and (x^2) - (y^2) =1 at their point of intersection in the first quadrant. 3. The attempt at a solution I know what the derivatives of both functions are and what they look like when graphed. But, I'm not sure what to do with it beyond that. For the first function I have that dy/dx=-1/x^2 and for the second I have dy/dx = x/sqrt(-1+x^2). What is different about these functions and what happens in the first quadrant?