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 $A, B, C$ are parallel to the coordinates planes is

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

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

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

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

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Solution

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 $(a, b, c)$

$∴ \frac{a}{x_{1}} + \frac{b}{y_{1}} + \frac{c}{z_{1}} = 1$

$∴$ Locus of $(x_{1}, y_{1}, z_{1})$ is $\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 1$ .

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