Given, p be the length of perpendicular from the origin to the line whose intercepts on the axes are a and b is

x

a

+

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 =

|b×0+a×0−ab|

√b2+a2

⇒ p2 =

a2b2

a2+b2

⇒

1

p2

a2+b2

a2b2

⇒

1

p2

=

a2

a2b2

+

b2

a2b2

⇒

1

p2

=

1

a2

+

1

b2