The equation of a curve is \(\dfrac{x^2}{2}+(y-k)^2=2\), where \(k\) is a constant.
Find the set of values of \(k\) for which the line \(y=2x\) meets this curve.[5]
In the case where the line \(y=2x\) is tangent to the curve, deduced the value(s) of \(k\), giving your answer in the form of \(a\sqrt b\) where \(a\) and \(b\) are integers.[1]
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