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A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is `1/x^2+1/y^2+1/z^2=1/p^2`.

A

`x^(-1)+y^(-1) + z^(-1) =p^(-1)`

B

`x^(-2) +y^(-2) +z^(-2)=p^2`

C

`x +y + z = p`

D

`x^2 +y^2 + z^2=p^2`

Text Solution

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The correct Answer is:
B
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