Question

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

Answer 1

Correct Answer - D

Let the point R be (h,k) .
thus `P-=(h,0) and Q-=(0,k)`
Equation of variable line `PQ is (x)/(h)+(y)/(k)=1`
Point `A(2,3)` lies on the variable line PQ
`therefore (2)/(h)+(3)/(k)=1`
or `(2)/(x)+(3)/(y)=1`
Therefore, the locus of point R is `2y+3x=xy`.