Question

Suppose the tangent line at a point P on the hyperbola xy = 3, cuts the
x-axis at point A and the y-axis at point B.
(a) Show that P is the mid-point of the line segment AB.
(b) If O is the origin, show that the triangle OAB formed by the tangent
line and the coordinate axes always has the same area, no matter where
P is located on the hyperbola.