Question

A straight rod of length 3l units slides with its ends A, B always on the x and y axes respectively then the locus of centroid of $△OAB$ is

• A. $x^2+y^2=3l^2$
• B. $x^2+y^2=l^2$
• C. $x^2+y^2=4l^2$
• D. $x^2+y^2=2l^2$

Answer 1

The correct option is B $x^2+y^2=l^2$

Let OA= a, OB = b, AB = 3
A = (a, 0), B = (0, b)
Let G(x,y) = $(\frac{a}{3},\frac{b}{3})$, a = 3x, b = 3y
$a^2+b^2=9l^2\Rightarrow x^2+y^2=l^2$