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