Hyperbola

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