The hyperbola is $ \frac{x^2}{4} - \frac{y^2}{9} = 1 $
Auxilliary circle is the circle between the two curves of hyperbola.
$\therefore \:\: (a, 0)$ and $(- a, 0)$ touches the circle with centre (0, 0)
$\therefore $ Equation of circle is
$\left(x-0\right)^{2} + \left(y-0\right)^{2} = \left(\sqrt{\left(a-0\right)^{2} + \left(0-0\right)^{2}}\right)^{2} $
$\Rightarrow x^{2} +y^{2} =a^{2} $
So, $x^{2} +y^{2} = 4 $ $(\because \:\: a = 2)$
