Let A(0,1), B(1,1) and C(1,0) be the mid...

Let `A(0,1), B(1,1) and C(1,0)` be the mid-points of the sides of a triangle with incentre at the point D. If the focus of the parabola `y^2=4ax` passing through D is `(alpha+betasqrt2,0)`, where `alpha` and `beta` are rational number, then `alpha/beta^2` is equal to

`9/2`

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