Hyperbola C2: \(\frac{(x-a)^2}{9}-\frac{(y-0)^2}{4}=1\)

On the x-axis y = 0, and the values of x are: \(x = a\pm3\) so \(x=a\) is the value half way between the two parts of the curve.

The two asymptotes cross at this half-way point, so from \(y=\frac{2}{3}x-2\) we have \(x = 3\) when y = 0.

So \(a = 3\)