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:

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Let the equation of line be x a + y b = 1 . . . . . . . 1 Clearly P a , 0 and Q 0 , b . Also h = a , k = b Now 1 passes through 2 , 3 ⇒ 2 a + 3 b = 1 ⇒ 2 h + 3 k = 1 Hence, locus is 3 x + 2 y = x y

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