Prove that if a plane has the intercepts `a ,\ b ,\ c\ a n d\ ` is at a distance of `p` units from theorigin, then `1/(a^2)=1/(b^2)+1/(c^2)=1/(p^2)dot`

Explanation

Equation of a plane which cuts the interceptors, a, b and c on axes is,
`x/a+y/b+z/c=1 rArr (1/a) x+ (1/b)y+(1/c)z-1 = 0`
Given, that the distance of plane from origin is p.
`:. p = |(1/a*0+1/b*+1/c*0-1)/(sqrt((1/a)^(2)+(1/b)^(2)+(1/c)^(2)))|`
`rArr 1/p = sqrt((1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2)))`
`rArr (1)/(p^(2))=(1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))`