A variable plane passes through a fixed point and cuts the coordinate axes at points and

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

A variable plane passes through a fixed point

(a, b, c)

and cuts the coordinate axes at points

A, B

and

C

. Show that the locus of the centre of the sphere

OABC

\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 2