A curve has equation \(y=x^{2}-8 x+c\), where \(c\) is a constant. (a) Find the value of \(c\) in each of the following cases. (i) The curve crosses the \(x\)-axis at \(x=2\).

(ii) The minimum value of \(y\) is 3 .

(b) Find the range of values of \(c\) for which \(y\) is always greater than 0 .