Question

The length of the lactusrectum of the ellipse $16x^2+25y^2=400$ is :

• A. $\frac{5}{16}$ unit
• B. $\frac{32}{5}$ unit
• C. $\frac{16}{5}$ unit
• D. $\frac{5}{32}$ unit

Answer 1

The correct option is B $\frac{32}{5}$ unit

Given equation can be rewritten as
$\frac{x^2}{25}+\frac{y^2}{16}=1$
Here, $a^2=25,b^2=16$
$\therefore$ Length of latusrectum $=\frac{2b^2}{a}$
$=\frac{2\times 16}{5}=\frac{32}{5}$