AP EAMCET · Maths · Circle
If a circle of a constant radius 6 passes through origin \(O\) and meets the coordinate axes at \(A\) and \(B\), then find the locus of the centroid of \(\triangle O A B\).
- A \(x^2+y^2=4\)
- B \(x^2+y^2=36\)
- C \(x^2+y^2=16\)
- D \(x^2+y^2=6\)
Answer & Solution
Correct Answer
(C) \(x^2+y^2=16\)
Step-by-step Solution
Detailed explanation
Let \((h, k)\) be centroid of triangle \(\therefore \quad h=\frac{a}{3}\) and \(k=\frac{b}{3}\) \(a=3 h, b=3 k\) Now, \(A B\) is diameter of circle. \(\begin{aligned} \therefore & a^2+b^2=144 \\ \therefore & (3 h)^2+(3 k)^2=144 \Rightarrow h^2+k^2=\frac{144}{9}\end{aligned}\)…
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