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

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) x2+y2=3 (B) x2+y2=9 (C) x2+y2=1 (D) x2+y2=81

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/afbe72d13c5192e2cda14ef02788a8cf-.png" /> Let end A is (a, 0) and end B is (0, b) then a2+b2=81 ldots (1) If centroid is (x, y) then x=(a/3), y=(b/3), putting in (1) we get the locus as x2+y2=9

Q. 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 $△ O A B$ is

$x^{2} + y^{2} = 3$

$x^{2} + y^{2} = 9$

$x^{2} + y^{2} = 1$

$x^{2} + y^{2} = 81$

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

Q. 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 △OAB is

x2+y2=3

x2+y2=9

x2+y2=1

x2+y2=81