Question

A straight rod of length $9$ units slides with its ends $A, B$ always on the $X$ and $Y$-axis respectively. Then the locus of the centroid of $\triangle O A B$ is

• A. $x^{2}+y^{2}=3$
• B. $x^{2}+y^{2}=9$
• C. $x^{2}+y^{2}=1$
• D. $x^{2}+y^{2}=81$

Answer 1

Answer: (B)

Let end $A$ is $(a, 0)$ and end $B$ is $(0, b)$ then
$a^{2}+b^{2}=81 \ldots$ (1)
If centroid is $(x, y)$ then
$x=\frac{a}{3}, y=\frac{b}{3}$, putting in (1)
we get the locus as $x^{2}+y^{2}=9$