Q93 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics
The length of the latus rectum of $16 x^2+25 y^2=400$ is
- A$\frac{25}{2}$
- B$\frac{25}{4}$
- C$\frac{16}{2}$
- Correct answerD$\frac{32}{5}$
Solution
$\begin{aligned}
& 16 x^2+25 y^2=400 \Rightarrow \frac{x^2}{25}+\frac{y^2}{16}=1 \\
a^2= & 25, b^2=16
\end{aligned}$
Length of lectus rectum $=\frac{2 b^2}{a}=\frac{32}{5}$
Length of lectus rectum $=\frac{2 b^2}{a}=\frac{32}{5}$
Hence, the correct answer is option: 'D'.