A calculus problem by Rocco Dalto

Calculus Level pending

The graph of $${\bf 4 x^2 + 12 xy + 9 y^2 + 8 \sqrt{13} x + 12 \sqrt{13} y - 65 = 0 }$$ are two parallel lines. 

If one line is represented by $${\bf a\sqrt{b} \:x + c\sqrt{b} \:y + b = 0 }$$ and the other line is represented by $${\bf ax + cy + d\sqrt{b} = 0, }$$ where $${\bf gcf(|a|,|b|,|c|,|d|) = 1, }$$ 

Find: $${\bf |a| + |b| + |c| + |d|. }$$

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