Interesting Locus Problem

Geometry Level 4

Consider the ellipse: \( \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \) If the locus of the middle points of a system of parallel chords of this ellipse is a line with slope \(m\) and can be written in the form: \( y = - \frac{b^{\alpha}}{a^{\beta}m^{\gamma}}x \) Find the value of: \( \alpha+\beta+\gamma \)

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