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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

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2x+3y=xy

3x+2y=xy

3x+2y=6xy

3x+2y=6

answer is B.

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Detailed Solution

$\frac{x}{h} + \frac{y}{k} = 1$ passes through(2,3)

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

Locus: $\frac{2}{x} + \frac{3}{y} = 1$

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