Question

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axes at A and B, P is the mid-point of AB. The curve passes through the point (1, 1). Determine the equation of the curve.

Answer 1

The equation of the tangent at any point (x, y) on the curve is

It is given that,

which is passing through (1, 1), then c = 1. 

Hence, the equation of the curve is 

xy = 1.