The Hyped Hyperbola

Geometry Level pending

The graphs of the curves\( { x }^{ 2 }\quad -\quad { y }^{ 2 }\quad +\quad 6x\quad +\quad 16y\quad -\quad 46\quad =\quad 0\) and \({ x }^{ 2 }\quad +\quad { y }^{ 2 }\quad +\quad 6x\quad -\quad 24y\quad +\quad 72\quad =\quad 0\) intersect in four points. Find the sum of the distances of the points from \((-3,2) \).

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