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If a variable plane which is at a constant distance 3p from the origin cut the co-ordinate axes at points A ,B , C , then locus of the centroid of `DeltaABC` is

A

`(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(9p^(2))`

B

`(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(3p^(2))`

C

`(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2))`

D

`(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(3)/(p^(2))`

Text Solution

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The correct Answer is:
C
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