A variable line, drawn through the point of intersection of the straight lines \( \frac{x}{a}+\f...

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A variable line, drawn through the point of intersection of the straight lines \( \frac{x}{a}+\frac{y}{b}=1 \) and \( \frac{x}{b}+\frac{y}{a}=1 \), meets the coordinate axes in \( A \) \& \( B \). Show that the locus of the mid point of
\( \mathrm{P} \) \( A B \) is the curve \( 2 x y(a+b)=a b(x+y) \).

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