Minimum distance...

Algebra Level 4

{x2+y2+6x12y+20=0y2=4x\begin{cases} { x }^{ 2 }+{ y }^{ 2 }+6x-12y+20=0 \\ { y }^{ 2 }=4x \end{cases}

The shortest distance between the above curves can be written in the form abc a\sqrt { b } -c , then find a+b+c a+b+c .

Note: a a ,b b and c c are positive integers and b b is not a perfect square.

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