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 $y=\frac{b}{e}$
$=\frac{5}{3/5}=\frac{25}{3}$