A variable plane which remains at a constant distance 3p from the orig – InterviewSolution

1.	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 1x2+1y2+1z2=1p2
Answer» A variable plane which remains at a constant distance $3 p$ from the origin cuts the coordinate axes at $A, B, C$ . Show that the locus of the centroid of triangle $A B C$ is $\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = \frac{1}{p^{2}}$

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