Question

A variable straight line passes through a fixed point $(a, b)$ intersecting the co-ordinates axes at $A \& B$. If ' $O$ ' is the origin, then the locus of the centroid of the triangle $OAB$ is :

• A. $b x+a y-3 x y=0$
• B. $b x+a y-2 x y=0$
• C. $a x+b y-3 x y=0$
• D. $a x+b y-2 x y=0$

Answer 1

Answer: (A)

equation of line $A B$
$y-b=m(x-a)$

$\therefore G \left(\frac{ a -\frac{ b }{ m }}{3}, \frac{ b - am }{3}\right)$
$ \Rightarrow h =\frac{ a -\frac{ b }{ m }}{3}, k =\frac{ b - am }{3}$
on eleminating ' $m$ ' we get required locus
$b h+a k-3 h k=0 \Rightarrow b x+a y-3 x y=0$