If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that `1/(p^2)=1/(a^2)+1/(b^2)`.

Explanation

Equation of line
`(x)/(a)+(y)/(b)=1implies(x)/(a)+(y)/(b)-1=0`
Length of perpendicular drawn from origin to this line is,
`p=|(0+0-1)/(sqrt((1)/(a^(2))+(1)/(b^(2))))|`
`implies p^(2)=(1)/((1)/(a^(2))+(1)/(b^(2)))implies (1)/(p^(2))=(1)/(a^(2))+(1)/(b^(2))`