When \(\lg y\) is plotted against \(x^2\), a straight line graph is obtained which passes through the points \((2,4)\) and \((6,16)\).

(i) Show that \(y=10^{A+Bx^2}\), where \(A\) and \(B\) are constants.

(ii) Find \(y\) when \(x=\frac1{\sqrt3}\).

(iii) Find the positive value of \(x\) when \(y=2\).