If a plane has intercepts a,b,c on axes and is at a distance of p units from the origin then prove that `1/a^2+1/b^2+1/c^2=1/p^2`

Explanation

We know that the equation of the plane which makes intercepts a, b and c on the axes is
`x/a+y/b+z/c=1 rArr x/a+y/b+z/c-1=0`……..(i)
It is given that p is the length of perpendicular drawn from O(0,0,0) to the plane (i).
`therefore p=(|0+0+0|)/sqrt(1/a^(2)+1/b^(2)+1/c^(2))=1/p rArr 1/a^(2)+1/b^(2)+1/c^(2) =1/p^(2)`.
Hence, `1/a^(2)+1/b^(2)+1/c^(2)=1/p^(2)`.