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
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
Updated On: Jun 14, 2022
- a parabola
- a circle
- an ellipse
- a pair of straight lines
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The Correct Option is B
Solution and Explanation
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.
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.
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