Equation of plane passing through points
$(\mathrm{p}, 0,0),(0, \mathrm{q}, 0)$ and $(0,0, \mathrm{r})$ is $\frac{\mathrm{x}}{\mathrm{p}}+\frac{\mathrm{y}}{\mathrm{q}}+\frac{\mathrm{z}}{\mathrm{r}}=1$
Given that this plane passes through $(\mathrm{a}, \mathrm{b}, \mathrm{c})$.
$\therefore \frac{a}{p}+\frac{b}{q}+\frac{c}{r}=1$
Equation of sphere is $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}-\mathrm{px}-\mathrm{q} y-\mathrm{rz}=0$.
Centre of the sphere $=(1, \mathrm{~m}, \mathrm{n})=\left(\frac{\mathrm{p}}{2}, \frac{\mathrm{q}}{2}, \frac{\mathrm{r}}{2}\right)$
$\Rightarrow \mathrm{p}=2 \ell, \mathrm{q}=2 \mathrm{~m}, \mathrm{r}=2 \mathrm{n}$
$\therefore$ locus of the centre $\Rightarrow \frac{\mathrm{a}}{\mathrm{x}}+\frac{\mathrm{b}}{\mathrm{y}}+\frac{\mathrm{c}}{\mathrm{z}}=2$.