Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Let $\mathrm{A}\equiv (\mathrm{a},0,0),\mathrm{B}\equiv (0,\mathrm{b},0),\mathrm{C}\equiv (0,0,\mathrm{c})$, then equation of the plane is $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$ Its distance from the origin, $\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{p^2}\dots$ (i) If $(x,y,z)$ be centroid of $\Delta ABC$, then $$\mathrm{x}=\frac{\mathrm{a}}{3},\mathrm{y}=\frac{\mathrm{b}}{3},\mathrm{z}=\frac{\mathrm{c}}{3}...(ii)$$ Eliminating a,b,c from (i) and (ii) required locus is $x^{-2}+y^{-2}+z^{-2}=9p^{-2}$