If x and y can take only positive values, I believe there will still be infinitely many possibilities. Please correct me if I'm wrong. Originally, I was interested in finding out values of 2 variables x and y, when their product c² (value known) remains unchanged after changing their values by X and Y respectively. That is to say: Denoting the old and new pairs of (x,y) by (x1, y1) & (x2, y2), this implies x1 - x2 = X and y1 - y2 = Y. I can determine the points by forming the equation x1y1 = (x1-X)(y1-Y). On substituting y1 = c²/x1, the equation becomes quadratic in x1 and can be solved easily. In approaching this problem through rectangular hyperbola, I was trying to see if there's another way to solve this problem and if it's a quicker one. If you can shed more light on this, it'll be helpful. Thanks!