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 \[AB\] is

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

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

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

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

If a variable line drawn through the point of intersection of straight

1.	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 \[AB\] is
A.	\[\alpha \beta (x+y)=xy(\alpha +\beta )\]
B.	\[\alpha \beta (x+y)=2xy(\alpha +\beta )\]
C.	\[(\alpha +\beta )(x+y)=2\alpha \beta xy\]
D.	None of these
Answer» C. \[(\alpha +\beta )(x+y)=2\alpha \beta xy\]

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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 \[AB\] is

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