A variable plane is at constant distance 3 from origin and meets the axis in `X,Y,Z` planes through `X,Y,Z` parallel to coordinate planes are made. If `P`be the point of intersection of above made planes, given `P(alpha, beta, gamma)` then `(alpha beta gamma)/(sqrt(alpha^(2)beta^(2)+beta^(2)gamma^(2)+gamma^(2)alpha^(2)))=?`

Answer

3

Explanation

`:'` Plane is `x/a+y/b+z/c=1`
Distance from `(0,0,0)=3` is
`1/(sqrt(1/(a^(2))+1/(b^(2))+1/(c^(2))))=3`
`:.` Locus of `P` is `1/(x^(2))+1/(y^(2))+1/(z^(2))=1/9`