Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Let the plane be $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$, meeting the axes at $A(a,0,0),B(0,b,0),C(0,0,c)$. The centroid is $\left(\frac{a}{3},\frac{b}{3},\frac{c}{3}\right)=\left(1,r,r^2\right)$, so $a=3,b=3r,c=3r^2$. The plane is $\frac{x}{3}+\frac{y}{3r}+\frac{z}{3r^2}=1$, i.e. $r^{2}x+ry+z=3r^2$.