Conic section

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 $a = 3$