A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes

Let the line be $y=m x+c$

$\mathrm{x}$-intercept : $-\frac{\mathrm{c}}{\mathrm{m}}$

y-intercept : c

A.M of reciprocals of the intercepts :

$\frac{-\frac{\mathrm{m}}{\mathrm{c}}+\frac{1}{\mathrm{c}}}{2}=\frac{1}{4} \Rightarrow 2(1-\mathrm{m})=\mathrm{c}$

line $: y=m x+2(1-m)=c$

$\Rightarrow \quad(\mathrm{y}-2)-\mathrm{m}(\mathrm{x}-2)=0$

$\Rightarrow$ line always passes through $(2,2)$

Ans. 4