A variable plane is at a constant distance p from the origin and meets the axes in A,B and C. The locus of the centroid of the triangle ABC is

Tips and Trickes 7(i) $\Rightarrow \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1;$

$A(a,0,0),B(0,b,0),C(0,0,0),(x,y,z)=\left(\frac{a}{3},\frac{b}{3},\frac{c}{3}\right)$

$a=3x,b=3y,c=3z,\frac{x}{x_1}+\frac{y}{y_1}+\frac{z}{z_1}=3\text{; }$

$p=\frac{1-31}{\sqrt{\frac{1}{x_1^2}+\frac{1}{y_1^2}+\frac{1}{z_1^2}}}\Rightarrow \frac{1}{x_1^2}+\frac{1}{y_1^2}+\frac{1}{z_1^2}=\frac{9}{p^2}$