Question

The equation of a directrix of the ellipse $\frac{x^2}{16}+\frac{y^2}{25}=1$

• A. $y=\frac{25}{3}$
• B. x = 3
• C. x = - 3
• D. $x=\frac{3}{25}$

Answer 1

Answer: (A)

$a^{2}=16, b^{2}=25$.
Since $a^{2}=b^{2}\left(1-e^{2}\right)$
$ \therefore 16=25\left(1-e^{2}\right) $
$\therefore 1-e^{2}=\frac{16}{25} $
$ \Rightarrow e^{2} = \frac{9}{25} $
$ \Rightarrow e=\frac{3}{5} $
$ \therefore $ One directrix is $y=\frac{b}{e} $
$= \frac{5}{3/5} =\frac{25}{3}$