# There Are Only Two!

Geometry Level 3

There exist two ordered triples $$(a,b,c)$$ for which $$4x^2-4xy+ay^2+bx+cy+1=0$$ represents a pair of identical straight lines in $$x$$-$$y$$ plane.

If these triples are $$(a_1,b_1,c_1)$$ and $$(a_2,b_2,c_2)$$, then find the value of $$a_1+b_1+c_1+a_2+b_2+c_2$$.

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