CircleHard
Question
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 PAS as P moves on the circle is
Options
A.a parabola
B.a circle
C.an ellipse
D.a pair of straight lines
Solution
Choosing OA as x-axis,A = (r, 0), B = (0, r) and any point P on the circle is (r cos θ, r sin θ)
If the centroid of ᐃPAB, the
3x = r cos θ + r + 0
and 3y = r sin θ + 0 + r
∴ (3x - r)2 + (3y - r)2 = r2
Hence, locus of P is a circle.
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