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

Options

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

Answer

B

Explanation

Choosing OA as X-axis, A = (r,0), B=(0,r) and any point P on the circle is (r `cos theta , r sintheta)` If (x,y) is the centroid of `DeltaPAB`, then

`3x=rcos theta+r+0`
`and 3y = r sintheta+0+r`
`therefore (3x-r)^(2)+(3y-r)^(2)=r^(2)`
Hence, locus of P is a circle.