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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:
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The correct answer is:
$x^{2}+y^{2}=9$
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
$x^{2}+y^{2}=9$
$\mathrm{a}^{2}+\mathrm{b}^{2}=81$
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
$x^{2}+y^{2}=9$
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