Question

Find the co-ordinates of foci, the eccentricity, and the latus rectum. Determine also the equation of its directrices for the given hyperbola:

$4x^2-9y^2=36$

Answer 1

$\frac{x^2}{9}-\frac{y^2}{4}=1$

$\therefore a^2=9,b^2=4$

$b^2=a^2(e^2-1)$

$\therefore e=\frac{\sqrt{\left(13\right)}}{3}$

Foci$(\pm ae,0),i.e(\pm \sqrt{13},0)$

L.R. $=\frac{2b^2}{a}=\frac{8}{3},$

Directricies $x=\pm \frac{a}{e}=\pm \frac{9}{\sqrt{13}}.$