Question

A variable plane passes through the fixed point (a, b, c) and meets the axes at A, B, C. The locus of the point of
intersection of the planes through A, B, C and parallel to the coordinate planes is

• A. $\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=2$
• B. $\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=1$
• C. $\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=-2$
• D. $\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=-1$

Answer 1

The correct option is B $\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=1$

Let plane is $\frac{x}{x_1}+\frac{y}{y_1}+\frac{z}{z_1}=1$
which passes through (a, b, c)
$\therefore \frac{a}{x_1}+\frac{b}{y_1}+\frac{z}{z_1}=1$
$\therefore Locusof(x_1,y_1,z_1)$ is
$\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=1$