Question

If a circle of constant radius 3k passes through the origin and meets the axes at A and B, the locus of centroid of DOAB is-

• A. x² + y² = k²
• B. x² + y² = 2k²
• C. x² + y² = 3k²
• D. x² + y² = 4k²

Answer 1

Answer: (D)

x² + y² = 4k²

Answer 2

Let centroid is (a, b)

a = a/3 ̃ a = 3a , b = b/3 ̃ b = 3b

radius = $\frac{AB}{2}$

3k = $\frac{\sqrt{a^{2} + b^{2}}}{2}$

̃ 6k = $\sqrt{9\alpha^{2} + 9\beta^{2}}$

a² + b² = 4k²