I used algebra approach for this question.
So the circle will intersect with y-axis at point \((0,y_0)\).
Substitute into the question we have: \(a^2 + (y_0 - b)^2 = 16 <-> a^2 - 16 + (y_0 - b)^2 = 0\)
--> so the question is whether this equation have real root \(y_0\) or not.
(1) Lead to: \(a^2 - 16\) can be >0 or <0
--> insufficient(2) Lead to: \(a^2 - 16 >0 -> a^2 - 16 + (y_0 - b)^2 > 0\): equation has no real root \(y_0\) -->
no intersect: sufficient.
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