If h denotes the arithmetic mean and k denotes the geometric mean of the intercepts made on  the coordinate axes by the lines passing through the point (1, 1), then the point (h, k)  lies on

Let the equation of the line be xa+yb=1 If it passes through (1, 1), then 1a+1b=1⇒  a+b=abSince the line makes intercepts of lengths a and b on the  coordinate axes, we haveh=a+b2  and k=abso that from (i) we get 2h=k2 and thus the point (h, k)lies on 2x=y2 which is a parabola.