Given, p be the length of perpendicular from the origin to the line whose intercepts on the axes are a and b is $\frac{x}{a}+\frac{y}{b}$ = 1 or bx + ay – ab = 0 ... (i) Since p is the length of perpendicular from origin upon the line (i), we have p = $\frac{\left|b\times0+a\times0-ab\right|}{\sqrt{b^2+a^2}}$ ⇒ $p^2$ = $\frac{a^2b^2}{a^2+b^2}$ ⇒ $\frac{1}{p^2}$ $\frac{a^2+b^2}{a^2b^2}$ ⇒ $\frac{1}{p^2}$ = $\frac{a^2}{a^2b^2}+\frac{b^2}{a^2b^2}$ ⇒ $\frac{1}{p^2}$ = $\frac{1}{a^2}+\frac{1}{b^2}$