A straight line through a fixed point 2 , 3 intersects the coordinate axes at distinct points P and Q . If O…

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:
  1. 3x+2y=6xy
  2. 3x+2y=6
  3. 2x+3y=xy
  4. 3x+2y=xy

Solution

Let the equation of line be xa+yb=1   .......1

Clearly Pa,0 and Q0,b. Also h=a, k=b

Now 1 passes through 2,3

⇒2a+3b=1

⇒2h+3k=1

Hence, locus is 3x+2y=xy

Asked in: JEE Main 2018 (08 Apr)

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