A variable plane moves so that the sum of reciprocal of its intercepts on the three coordinate axes is constant λ. It passes through a fixed point, which has coordinates:
(1λ,1λ,1λ)
Let the equation of the variable is xa+yb+zc=1 ...(1)
The intercept on the coordinate axes are a,b,c.
The sum of reciprocals of intercepts is constant λ, therefore
1a+1b+1c=λ⇒(1/λ)a+(1/λ)b+(1/λ)c=1
∴(1λ,1λ,1λ) lies on the plane (1)
Hence, the vatiable plane (1) always passes through the fixed point (1λ,1λ,1λ)