A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

Explanation

`x/a+y/b=1`

`1/a+1/b=alpha`

`1/a=alpha-1/b`

`(alpha-1/b)x+y/b=1`

`1/b(y-alpha)+(alphax-1)=0`

`alpha^2-1=0`

`L_1=y=lambda=0`

`y=1/lambda(11/alpha,1/alpha)`.