Question

A straight rod of the length 6 units, slides with its ends A and B always on the x and y axes respectively. If O is the origin, then find the locus of the centroid of ∆OAB.​

Answer 1

Answer:

Let the coordinates of ends of rod be A(a,0),B(0,b)

AB=9⟹a2+b2=81⋯(1)

Let the centroid of the △OAB be (h,k)

h=30+a+0=3a,k=30+0+b=3b

⟹a=3h,b=3k

From (1),(3h)2+(3k)2=81⟹h2+k2=9

The locus of centroid of  △OAB is x2+y2=9

Answer 2

${x}^{2} + {y}^{2} = {6}^{2}$

$x = 6 \cos( \alpha )$

$y = \: 6 \sin( \alpha )$

C = ( x/3 , y/3)...