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The straight line through a fixed point ...

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=6`

B

`2x+3y=xy`

C

`3x+2y=xy`

D

`3x+2y=6xy`

Text Solution

Verified by Experts


Equation of line `PQ` is `(x)/(alpha)+(y)/(beta)=1`
Since this line is passes through fixed point `(2,3)`
`:. (2)/(alpha)+(3)/(beta)=1`
`:.` Locus of `R` is
`2beta+3alpha=alphabeta`
i.e.`2y+3x=xyimplies3x+2y=xy`
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