Conic Sections Question 485
Question: If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at A and B, then the locus of the centroid of triangle OAB is
Options:
A) $ x^{2}+y^{2}={{(2k)}^{2}} $
B) $ x^{2}+y^{2}={{(3k)}^{2}} $
C) $ x^{2}+y^{2}={{(4k)}^{2}} $
D) $ x^{2}+y^{2}={{(6k)}^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let the centroid of triangle OAB be (p, q).
Hence, points A and B are (3p, 0) and (0, 3q), respectively. But diameter of the circle, AB=6k
Hence, $ \sqrt{9p^{2}+9q^{2}}=6k $ Therefore, the locus of (p, q) is $ x^{2}+y^{2}=4k^{2} $ .
BETA
