Mathematics - Ellipse Question with Solution | TestHub

Given curves $C_1:x^2-y^2=1(x<0)$ and $C_2:xy=1(y>0)$. An ellipse $C_3$ shares a focus with $C_2$, and the corresponding directrix is an asymptote of $C_1$. The major-axis length of $C_3$ is 8/3. Find the eccentricity of $C_3$.