# 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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