Question

Find the eccentricity and length of the latus rectum of the hyperbola $16x^2-9y^2=144.$

Answer 1

Given equation of hyperbola-

$16x^2-9y^2=144$

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

Here $a=3,b=4$

Now,

Eccentricity $\left(e\right)=\pm \sqrt{1+\frac{b^2}{a^2}}=\pm \sqrt{1+\frac{16}{9}}=\pm \frac{5}{3}$

Length of latus rectum $\left(l\right)=\frac{2b^2}{a}=\frac{2\times 16}{3}=\frac{32}{9}$

Hence the eccentricity and length of latus rectum of the given hyperbola is $\pm \frac{5}{3}$ and $\frac{32}{9}$ respectively.