CircleHardBloom L3
Question
If a circle of constant radius $3k$ passes through the origin ' $O$ ' and meets coordinate axes at $A$ and $B$ then the locus of the centroid of the triangle $OAB$ is:
Options
A.$x^{2} + y^{2} = (2k)^{2}$
B.$x^{2} + y^{2} = (3k)^{2}$
C.$x^{2} + y^{2} = (4k)^{2}$
D.$x^{2} + y^{2} = (6k)^{2}$
Solution
Sol. [Key Concept: A radius-$3k$ circle through $O$ meeting the axes: same elimination gives the centre's locus.]
$$\begin{matrix} (3h)^{2} + (3k)^{2} = (6k)^{2} \\ h^{2} + k^{2} = 4k^{2} \end{matrix}$$
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