Question
Question: Let AB be a chord of the circle x<sup>2</sup> + y<sup>2</sup> = r<sup>2</sup> subtending a right ang...
Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre then the locus of the centroid of the triangle PAB as P moves on the circle is –
A
A parabola
B
A circle
C
An ellipse
D
A pair of straight line
Answer
A circle
Explanation
Solution
centroid of DPAB
h = 
, k = 
3h – r = r cos a, 3k – r = r sin a
(3h – r)2 + (3k – r) = r2
locus of (h, k)
(3x – r)2 + (3y – r)2 = r2