If 5x+9=0 is the directrix of the hyperbola 16x^2-9y^2=144, then its corresponding focus i…

Question

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

Accepted Answer

$\dfrac{x^2}9-\dfrac{y^2}{16}=1$, $a=3,b=4$, $e^2=1+\dfrac{16}9=\dfrac{25}9\Rightarrow e=\dfrac53$.

Directrix $x=-\dfrac95=-\dfrac ae$; the corresponding focus is $S'=(-ae,0)=\left(-3\cdot\dfrac53,0\right)=(-5,0)$.

Solutions · 1