question_answer

A variable straight line drawn through the point of intersection of lines \[\frac{x}{a}+\frac{y}{b}=1\]and \[\frac{x}{b}+\frac{y}{a}=1\]meets the coordinate axes at A and S. Then the locus of the mid-point of

A)  \[xy(a+b)=ab\,\,(x+y)\]

B)  \[2xy(a-b)=ab(x+y)\]

C)  \[2xy(a-b)=ab(x-y)\]

D)  \[2xy(a+b)=ab(x+y)\]