Question

The point (x, y) is on the curve xy = c² if and only if x = ct  and y = c/t  for some real number t. These equations are called parametric equation of xy = c² .

Answer 1

The point (ct,c/t) clearly lies on the curve xy = c²  . Conversely, if (x, y) is any point on the curve xy = c² , then take either t = x/c  or c/y. So x = ct and y = c/t .