Question

Let AB be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then, the locus of the centroid of the $\Delta PAB$ as P moves on the circle, is

• A. a parabola
• B. a circle
• C. an ellipse
• D. a pair of straight lines

Answer 1

Answer: (B)

a circle

Answer 2

Choosing OA as X-axis, A = (r,0), B = (0, r) and any
point P on the circle is (r $cos\theta$, r $sin\theta$). If (x, y) is the
centroid of $\Delta$ PAB, then
3x=r $cos\theta$ + r + 0
and 3y=r $sin \theta$ + 0 + r
$\therefore$ $(3x - r)^2 + (3y - r)^2 = r^2$
Hence, locus of P is a circle.