Question

A variable plane passes through the point (p, q, r) and meets the coordinate axis at point A, B and C. Show that the locus of a common point of plane passing through A, B and C and parallel to the coordinate planes, will be p/x + q/y + r/z = 1.

Answer 1

Let equation of plane is

Again plane meets the coordinate points.

Coordinates of points are (α,0,0) 

Coordinates of point B are (0, β, 0) and

coordinates of point C are (0, 0, γ) 

∴ Equation of planes, parallel to coordinate axis and passing through 

Point A is x = α …..(3) 

Point B is y = β …..(4) 

Point C is z = γ …..(5) 

∴ Locus of the point of intersection is

p/x + q/y + r/z = 1