A straight rod of length 9 units slides with its endsA, $B$ always on the $X$ and Y-axis respectively. Then…
A straight rod of length 9 units slides with its endsA, $B$ always on the $X$ and Y-axis respectively. Then the locus of the centroid of $\Delta \mathrm{OAB}$ is:
$x^{2}+y^{2}=3$
$x^{2}+y^{2}=9$
$x^{2}+y^{2}=1$
$x^{2}+y^{2}=81$
Solution
Let end $A$ is $(a, 0)$ and end $\mathrm{B}$ is $(0,$ b) then
$\mathrm{a}^{2}+\mathrm{b}^{2}=81$
If centroid is $(x, y)$ then
$\mathrm{x}=\frac{\mathrm{a}}{3}, \mathrm{y}=\frac{\mathrm{b}}{3},$ putting in (1) we get the locus as
$x^{2}+y^{2}=9$
