Question

Write the length of the latus-rectum of the hyperbola 16x² − 9y² = 144.

Answer 1

Equation of the hyperbola:
$16x^2-9y^2=144$
This equation can be rewritten in the following way:
$$\begin{gathered} \frac{16x^2}{144}-\frac{9y^2}{144}=1 \\ \Rightarrow \frac{x^2}{9}-\frac{y^2}{16}=1 \\ \Rightarrow \frac{x^2}{3^2}-\frac{y^2}{4^2}=1 \end{gathered}$$
This is the standard form of a hyperbola with $a=3$ and $b=4$.
Length of the latus rectum = $\frac{2b^2}{a}$
Substituting the value of a and b, we get:
Length of the ​latus rectum $=\frac{2\times 4^2}{3}=\frac{32}{3}$