The equation of a curve can be written as \(y=ax^2+b\) where \(a\) and \(b\) are constants.

Point \(A,B\) and \(C\) lie on the curve.

Given that

point \(A\) has coordinates \((2,11)\),

point \(B\) has coordinates \((0.5,3.5)\), and

point \(C\) lies on the \(y\)-axis.

Find the \(y\)-coordinate of the point \(C\).

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