Let the director circle of the hyperbola $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be denoted by $C_1$ and let director circle of ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{1}{3}$ be denoted $C_2$ . If the circle $C_2$ is also the director circle of  $C_1$ and let $e_1\text{and }{e}_2$  be the eccentricities of the ellipse E and hyperbola H, then  $\frac{e_2^2}{e_1^2}$ is equal to  $(a>b)$