A straight rod of length 9 units slides with its ends A,B always on the x and y axes respectively.then the locus of the centroid of triangle OAB is

Let the  co ordinates of centroid be (h,k).
h=(0+x1+0)/3

k=(0+0+y1)/3

so, x1=3h and y1=3k
Now length of the rod AB=9 units
 (Plot it on a paper and label the triangle AOB, where A=(x1,0) and B=(0,y1) )

Now in triangle OAB

OA²+OB²=AB²

x1²+y1²=9²

(SUBSTITUTE THE VALUE OF x1 and y1)

(3h)²+(3k)²=81

on dividing the whole of the above equation by 9 we get,

h²+k²=9

now replace h by x and k by  y to get the locus

therefore we get a circle of radius 3units

x²+y²=9   (Answer)