A) \[9\left( {{x}^{2}}+{{y}^{2}} \right)=4{{a}^{2}}\]
B) \[9\left( {{x}^{2}}+{{y}^{2}} \right)={{a}^{2}}\]
C) \[9\left( {{x}^{2}}+{{y}^{2}} \right)=2{{a}^{2}}\]
D) \[9\left( {{x}^{2}}+{{y}^{2}} \right)=8{{a}^{2}}\]
Correct Answer: A
Solution :
[a] Equation of circle \[\left( x-\alpha \right)\left( x-0 \right)+\left( y-0 \right)\left( y-\beta \right)=0\] \[{{x}^{2}}+{{y}^{2}}-\alpha x-\beta y=0\] \[a=\sqrt{\frac{{{\alpha }^{2}}}{4}+\frac{{{\beta }^{2}}}{4}}\] \[{{\alpha }^{2}}+{{\beta }^{2}}=4{{a}^{2}}\] Let centroid be (x, y) \[x=\alpha /3,\text{ }y=\beta /3\] \[\alpha =3x,\text{ }\beta =3y\] \[\therefore \text{ }locus\text{ }9\left( {{x}^{2}}+{{y}^{2}} \right)=4{{a}^{2}}\]You need to login to perform this action.
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