Q55 / 90 · JEE Main 2018 (08 Apr) · Mathematics

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 $O P R Q$ is completed, then the locus of $R$ is:

Solution

Let the equation of line be $\frac{x}{a} + \frac{y}{b} = 1 . . . . . . . (1)$

Clearly $P (a, 0)$ and $Q (0, b)$ . Also $h = a, k = b$

Now $(1)$ passes through $(2, 3)$

$\Rightarrow \frac{2}{a} + \frac{3}{b} = 1$

$\Rightarrow \frac{2}{h} + \frac{3}{k} = 1$

Hence, locus is $3 x + 2 y = x y$

Hence, the correct answer is option: 'D'.