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 focii is 3 times the distance between its directrices. Then $y^2-x^2=$

• A

  $\frac{23}{16}$
• Correct answer
  B

  $\frac{7}{4}$
• C

  $\frac{4}{7}$
• D

  $\frac{16}{23}$

Hence, the correct answer is option: 'B'.