JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let a circle of radius 4 pass through the origin O, the points A \( (-\sqrt{3}a,0) \) and \( B(0,-\sqrt{2}b) \), where a and b are real parameters and \( ab\ne0 \). Then the locus of the centroid of \( \Delta OAB \) is a circle of radius
- A \(\frac{5}{3}\)
- B \(\frac{7}{3}\)
- C \(\frac{8}{3}\)
- D \(\frac{11}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
AB=8 \(3 a^2+2 b^2=64\) Centroid G(h,k) \(\begin{array}{l}h=-\frac{\sqrt{3} a}{3}, k=-\frac{\sqrt{2} b}{3} \\ a=-\sqrt{3} h, b=\frac{-3}{\sqrt{2}} k\end{array}\) \(9 h^2+9 k^2=64\) \(x^2+y^2=\frac{64}{9}\) \(r =\frac{8}{3}\)
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