Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then `1/(a^2)+1/(b^2)+1/(c^2)=1/(p^2)`.

Explanation

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

\[ \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} = \frac{1}{p^2}, \]

we can follow these steps:

...