Find the given locus

Geometry Level 4

Locus of \(\text{mid-point of chords}\) of the parabola \(\large{y^2=4ax}\) that pass through the point \((3a,a)\) is

\[\large{py^2+qax+ray+sa^{2}=0}\]

Find the minimum value of \(p+q+r+s\)

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