A plane passes through a fixed point and cuts the axes in

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

A plane passes through a fixed point

(a, b, c)

and cuts the axes in

A, B, C

. The locus of a point equidistant from origin,

A, B

and

C

must be (1)

ayz + bzx + cxy = 2xyz

(2)

\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 1

(3)

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

(4)

\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 3