A straight line through a fixed point (2,3) intersects the coordinates axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is 3x+2y=6, xy, 2x+3y=xy, 3x+2y=xy

y−y1=m(x−x1) ⟹y−3=m(x−2)⟹mx−y−2m+3=0⟹mx−y=2m−3
X-intercept=2m−3m
Y-intercept=3−2m
⟹Co-ordinates of rectangle (0,0)⟹(2m−3m,0)⟹(0,3−2m)⟹Co-ordinates of R is (2m−3m,3−2m)⟹x=2m−3m y=3−2m
y=3−2m⟹m=3−y2
⟹x=2m−3m=2−3(3−y)2⟹x(3−y)=2(3−y)⟹3x−xy=6−2y⟹3x+2y=xy is the locus. options (1)