Mathematics · Coordinate Geometry

Let R be a rectangle bounded by the lines x = 0, x = 2, y = 0, and y = 5. Let A(α, 0) and B(0, β) where α &in; [0, 2] and β &in; [0, 5], be such that the line segment AB divides the area of the rectangle R in the ratio 4:1. Then, the locus of the mid-point of AB is a/an:

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Let R be a rectangle bounded by the lines x = 0, x = 2, y = 0, and y = 5. Let A(&alpha;, 0) and B(0, &beta;) where &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 locus of the mid-point of AB is a/an: