Q234 / 270 · NDA 2010 (Phase 1) · Mathematics
What are the equations of the directrices of the ellipse $25 x^2+16 y^2=400$ ?
- A$3 x \pm 25=0$
- B$3 y \pm 25=0$
- C$x \pm 15=0$
- Correct answerD$y \pm 25=0$
Solution
$\frac{25 x^2}{400}+\frac{16 y^2}{400}=1$
$\begin{gathered}
\quad \text { or } \frac{x^2}{16}+\frac{y^2}{25}=1 \\
\therefore \quad a^2=16, b^2=25
\end{gathered}$
$\therefore$ Eqs. of directrices are
$y \pm 25=0$
Hence, the correct answer is option: 'D'.