Question

Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P (x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.

Answer 1

Let’s take P(x , y) be any point on the curve and AB be the tangent to the given curve at P.

Also given, P is the mid-point of AB

So, the coordinates of A and B are (2x, 0) and (0, 2y) respectively.

The slope of the tangent AB = (2y – 0)/ (0 – 2x) = -y/x

Thus, the required equation is xy = 1