A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the three coordinate axes is constant. Show that the plane passes through a fixed point.

Explanation

Let equation of plane be
`x/a+y/b+z/c=1"……"(1)`
intercept on axes ` =a,b,c,`
Given that `1/a+1/b+1/c = k` where k is a scalar.
`rArr 1/(ka) + 1/(kb) + 1/( kc) = 1`
`rArr (1)/(a) (1/k) + 1/b(1/k) +1/c(1/k) = 1`
Therefore plane (1) passes through the point `(1/k,1/k,1/k)` which is fixed point.