Step 1 :

Let the equation of the line be $ \large\frac{x}{a}$$+\large\frac{y}{b}$$=1$

Its intercepts on the $x$ and $y$ axes are $a$ and $b$ respectively.

It is given that

$ \large\frac{1}{a}$$+\large\frac{1}{b}$ = constant = $k$ ( assume )

$ \therefore \large\frac{1}{ka}$$+ \large\frac{1}{kb}$$=1$

According to the given condition :

$ \large\frac{\Large\frac{1}{k}}{a}$$+\large\frac{\Large\frac{1}{k}}{b}$$=1$

Hence $ \large\frac{1}{k}$$,\large\frac{1}{k}$ satisfies the equation.

$ \large\frac{x}{a}$$+\large\frac{y}{b}$$=1$

Hence the line passes through the fixed point. $ \bigg( \large\frac{1}{k}$$, \large\frac{1}{k} \bigg)$