Question

A tangent to the curve y = f(x) cuts the line y = x at a point which is at a distance of one unit from y-axis. Find the equation of the curve.

Answer 1

The equation of the tangent at P(x, y) is

Y – y = (dy/dx)(X – x)

It cuts the line y = x, so the point of intersection

Integrating, we get

log |x – 1| = log |y – 1| + log c

log |(x – 1)/(y – 1)| = log c

(x – 1)/(y – 1) = c

which is the required equation of the curve