The Touch-Me-Not Parabola!

Geometry Level 4

If the least distance between parabola: \( y^2 = 4x \) and circle: \( x^2 + (y+12)^2 = 1 \) is of the form: \[ a\sqrt{b}-c \]

Find \( a + b+ c\).

Credits: My mathematics teacher.

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