Question

A circle with radius $2$ units passing through origin, cuts the $x-$ axis and $y-$ axis at $A$ and $B$ respectively. The locus of centroid of the triangle $OAB$ is

• A. $x^2+y^2=4$
• B. $x^2+y^2=\frac{16}{9}$
• C. $x^2+y^2=16$
• D. $x^2+y^2=9$

Answer 1

The correct option is B $x^2+y^2=\frac{16}{9}$


Let the centroid be $(x,y)$
Coordinates of
$A=(3x,0)B=(0,3y)$
We know that $AB$ is the diameter of the circle.
$AB=2r\Rightarrow \sqrt{(3x{)}^2+(3y{)}^2}=2\times 2\Rightarrow x^2+y^2=\frac{16}{9}$