Let $R$ be a rectangle given by the lines $x=0, x=2, y=0$ and $y=5$. Let $A(\alpha, 0)$ and $B(0, \beta), v \in[0,2]$ and $\beta \in[0,5]$, be such that the line segment $A B$ divides the area of the rectangle $R$ in the ratio $4: 1$. Then, the mid-point of AB lies on a
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