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  • If a circle of constant radius 3k passes through the origin 'O' and meets co-ordinate axes at A and B then the locus of the centroid of the triangle <img alt="\mathrm{OAB}" src="https://ent

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

Option: 1

\mathrm{x^{2}+y^{2}=(2 k)^{2}}


Option: 2

\mathrm{x^{2}+y^{2}=(3 k)^{2}}


Option: 3

\mathrm{x^{2}+y^{2}=(4 k)^{2}}


Option: 4

\mathrm{x^{2}+y^{2}=(6 k)^{2}}


Answers (1)

best_answer

 Given \mathrm{r}=3 \mathrm{k} and \mathrm{P} is centroid

\mathrm{g}^{2}+\mathrm{f}^{2}=(3 \mathrm{k})^{2}

\therefore \quad 3 \mathrm{~h}_{1}=\mathrm{a}$ and $3 \mathrm{k}_{1}=\mathrm{b}$ also $2 \sqrt{\mathrm{g}}=\mathrm{a} \Rightarrow 2 \mathrm{~g}=\mathrm{a}$ and $2 \mathrm{f}=\mathrm{b}

\Rightarrow \quad 2 \mathrm{~g}=\frac{3 \mathrm{~h}_{1}}{2}$ and $2 \mathrm{f}=\frac{3 \mathrm{k}_{1}}{2}\text{substitute in (1)}
\frac{9 \mathrm{~h}_{1}^{2}}{4}+\frac{9 \mathrm{k}_{1}^{2}}{4}=9 \mathrm{k}^{2} \quad \Rightarrow \quad \mathrm{x}^{2}+\mathrm{y}^{2}=(2 \mathrm{k})^{2}

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avinash.dongre

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