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A variable straight line is drawn throug...

A variable straight line is drawn through the point of intersection of the straight lines
`x/a+y/b=1` and `x/b+y/a=1` and meets the coordinate axes at `A` and `Bdot`
Show that the locus of the midpoint of `A B` is the curve `2x y(a+b)=a b(x+y)`

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