Question

A straight line through a fixed point $(2,3)$ intersects the coordinate axes at distinct points $P$ and $Q.$ If $O$ is the origin and the rectangle $OPRQ$ is completed, then the locus of $R$ is :

• A. $3x+2y=6xy$
• B. $3x+2y=6$
• C. $2x+3y=xy$
• D. $3x+2y=xy$

Answer 1

The correct option is D $3x+2y=xy$

Let $R(a,b)$ be the point.



Then equation of line be $\frac{x}{a}+\frac{y}{b}=1$
$\Rightarrow \frac{2}{a}+\frac{3}{b}=1$
$\therefore$ Locus of $R$ is
$\frac{2}{x}+\frac{3}{y}=1$
$\therefore 2y+3x=xy$