question_answer

If a variable line drawn through the point of intersection of straight lines \[\frac{x}{\alpha }+\frac{y}{\beta }=1\] and \[\frac{x}{\beta }+\frac{y}{\alpha }=1\] meets the coordinate axes in A and B, then the locus of the mid-point of A is

A)  \[(\alpha +\beta )(x+y)=2\,\alpha \beta xy\]

B)  \[\alpha \beta \,(x+y)=xy\,(\alpha +\beta )\]

C)  \[\alpha \beta \,(x+y)=2xy\,(\alpha +\beta )\]

D)  \[\alpha \beta \,(x-y)=2xy\,(\alpha -\beta )\]

E)  None of these