Minimum distance...

Algebra Level 5

\[\begin{cases} { x }^{ 2 }+{ y }^{ 2 }+6x-12y+20=0 \\ { y }^{ 2 }=4x \end{cases} \]

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

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

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