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about to only mathematics

A

a parabola

B

a circle

C

an ellipse

D

a pair of straight lines

Text Solution

Verified by Experts

The correct Answer is:
B
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.
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