Straight LineHardBloom L3
Question
A variable straight line passes through a fixed point ( $a,b$ ) intersecting the coordinate axes at $A\& B$. If ' $O$ ' is the origin, then the locus of centroid of triangle $OAB$ is :
Options
A.$bx + ay - 3xy = 0$
B.$bx + ay - 2xy = 0$
C.$ax + by - 3xy = 0$
D.$ax + by - 2xy = 0$
Solution
Sol. [Key Concept: Variable line through fixed $(a,b)$ meets the axes at $A,B$; eliminate to get the centroid locus.]
Equation of $AB$ is $\frac{x}{h} + \frac{y}{k} = 3$
$\because\ AB$ passes through $(a,b)$
$$\therefore\ \frac{a}{h} + \frac{b}{k} = 3 $$$\Rightarrow bx + ay = 3xy$ is the required locus.
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