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

Here, `a` and `b` are the intercepts on the axes. So, equation of line will be,

`x/a+y/b = 1`

Length of the perpendicular from origin this line `= |(a_1(0)+b_1(0)+c_1)/sqrt(a_1^2+b_1^2)|`

Here, `a_1 = 1/a, b_1 = 1/b and c_1 = -1`

So, ` |-1/sqrt(1/a^2+1/b^2 )| = p`

Squaring both sides,

`1/(1/a^2+1/b^2 ) = p^2`

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