A) \[\left( \frac{b}{3},\frac{b}{3} \right)\]
B) \[\left( \frac{2a}{3},\frac{2a}{3} \right)\]
C) \[\left( \frac{2b}{3},\frac{2b}{3} \right)\]
D) none of these
Correct Answer: C
Solution :
[c] Given \[ar\Delta AOC=2(ar\Delta BOC)\] Or \[\frac{1}{2}(OA)({{x}_{1}})=\frac{2\times 1}{2}(OB)({{x}_{1}})\] Or \[a=2b\] The equation of AB is \[\frac{x}{a}+\frac{y}{b}=1\] ...(i) Or \[\frac{x}{2b}+\frac{y}{b}=1\] ...(ii) Since point C lies on line (ii), we have \[\frac{{{x}_{1}}}{2b}+\frac{{{x}_{1}}}{b}=1\] Or \[{{x}_{1}}=\frac{2b}{3}=\frac{a}{3}\] Or \[C\equiv \left( \frac{2b}{3},\frac{2b}{3} \right)\]You need to login to perform this action.
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