We know that the length of the perpendicular from the point (a', b') to the line ax+by+c=0 is (aa'+bb'+c)/[sqrt(a^2+b^2)]

In our case a'=0, b'=0

and the line is x/a+y/b=1

thus substituting in the formula we get

(0+0-1)/[sqrt[(1/a^2)+(1/b^2)]= p

-1/sqrt[1/a^2+1/b^2] =p

resiprocating both the sides

sqrt[1/a^2+1/b^2]=1/p

square both the sides we get

1/a^2+1/b^2=1/p^2