If a plane has the intercepts \(a,b,c\) and is at a distance of \(p\) units from the origin, then

\(a^2+b^2+c^2=p^2\) \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=p^2\) \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{p^2}\) \(a^2+b^2+c^2=p\)

\(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{p^2}\)

Apply the distance formula