Let $x$ be the eccentricity of a hyperbola whose transverse axis is twice its conjugate axis. Let $y$ be the eccentricity of another hyperbola for which the distance between the foci is $3$ times the distance between its directrices. Then $y^2-x^2=$
- A$\frac{23}{16}$
- B$\frac{7}{4}$
- C$\frac{4}{7}$
- D$\frac{16}{23}$
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