Eccentricity of conjugate hyperbola of $16x^2 - 9y^2 - 32x - 36y - 164 = 0$ will be-

  • A

    $\frac{5}{3}$

  • B

    $\frac{5}{4}$

  • C

    $\frac{12}{5}$

  • D

    $\frac{13}{12}$

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  • [JEE MAIN 2022]

Find the coordinates of the foci and the vertices, the eccentricity,the length of the latus rectum of the hyperbolas : $\frac{x^{2}}{9}-\frac{y^{2}}{16}=1.$