Question

If a circle of constant radius $3k$ passes through the origin ${}^{\prime }{O}^{\prime }$ and meets co-ordinate axes at $A$ and $B$ then the locus of the centroid of the triangle $OAB$ is-

• A. $x^2+y^2={\left(2k\right)}^2$
• B. $x^2+y^2={\left(3k\right)}^2$
• C. $x^2+y^2={\left(4k\right)}^2$
• D. $x^2+y^2={\left(6k\right)}^2$

Answer 1

The correct option is A $x^2+y^2={\left(2k\right)}^2$

Let centroid of the triangle $OAB$ be $(\alpha ,\beta )$
$\therefore$ $a=3\alpha$, $b=3\beta$
And $a^2+b^2=9k^2$
$\Rightarrow$ $9{\alpha }^2+9{\beta }^2=9k^2$
$\therefore$ Locus of $(\alpha ,\beta )$ is $x^2+y^2=k^2$