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Question

A variable plane moves so that the sum of reciprocal of its intercepts on the three coordinate axes is constant λ. It passes through a fixed point, which has coordinates:

A
(λ,λ,λ)
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B

(1λ,1λ,1λ)

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C
(λ,λ,λ)
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D

(1λ,1λ,1λ)

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Solution

The correct option is B

(1λ,1λ,1λ)


Let the equation of the variable is xa+yb+zc=1 ...(1)

The intercept on the coordinate axes are a,b,c.

The sum of reciprocals of intercepts is constant λ, therefore

1a+1b+1c=λ(1/λ)a+(1/λ)b+(1/λ)c=1

(1λ,1λ,1λ) lies on the plane (1)

Hence, the vatiable plane (1) always passes through the fixed point (1λ,1λ,1λ)


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