A variable line passing through a fixed point ( , ) intersects the coordinate axes at A and B . If O is the origin, then the locus of the centroid of the O A B is

Step-by-step solution

Let points A(a, 0) and B(0, b) , so equation of variable line is x a + y b =1 Since the variable line (i) passes through the point ( , ) So, a + b =1 Now, centroid of O A B is ( a 3 , b 3 )=(h, k) So, a=3 h and b=3 k From Eqs. (ii) and (iii), we are getting 3 h + 3 k =1 On taking locus of point (h, k) , we are getting x+ y-3 x y=0 .