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A variable plane passes through a fixe...

A variable plane passes through a fixed point `(a,b,c)` and meets the axes at `A ,B ,a n dCdot` The locus of the point commom to the planes through `A ,Ba n dC` parallel to the coordinate planes is

A

contain point `(3,6,9)`

B

passes through `(0,0,0)`

C

is `1/x+1/y+1/z=1`

D

contains line `(x-1)/2=(y-2)/4=(z+6)/15`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `OA=x_(1),OB=y_(1),OC=z_(1)` be points on `X,Y,Z` axis then equation of plane is
`x/(x_(1))+y/(y_(1))+z/(z_(1))=1`
`implies1/(x_(1))+2/(y_(1))+3/(z_(1))=1`
`:.` Locus is `1/x+2/y+3/z=1`
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