If 5 x+9=0 is the directrix of the hyperbola

Question:

If $5 x+9=0$ is the directrix of the hyperbola $16 x^{2}-9 y^{2}=144$, then its corresponding focus is :

  1. $\left(-\frac{5}{3}, 0\right)$

  2. $(5,0)$

  3. $(-5,0)$

  4. $\left(\frac{5}{3}, 0\right)$


Correct Option: , 3

Solution:

$\frac{x^{2}}{9}-\frac{y^{2}}{16}=1$

$\mathrm{a}=3, \mathrm{~b}=4 \& \mathrm{e}=\sqrt{1+\frac{16}{9}}=\frac{5}{3}$

corresponding focus will be $(-$ ae, 0$)$ i.e., $(-5,0)$.

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