Question

The equation of the directrix of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ is/are

• A. $y=\frac{25}{4}$
• B. $y=-\frac{25}{4}$
• C. $x=-\frac{25}{4}$
• D. $x=\frac{25}{4}$

Answer 1

Answer: (C), (D)

The correct options are
C $x=-\frac{25}{4}$
D $x=\frac{25}{4}$

Given ellipse is $\frac{x^2}{25}+\frac{y^2}{9}=1$
Major axis is along the $x-$axis.
$a=5,b=3$
Hence, equation of the directrix are, $x=\pm \frac{a}{e}$
Finding $e$,
$e^2=1-\frac{b^2}{a^2}\Rightarrow e=\sqrt{\frac{16}{25}}=\frac{4}{5}$
Hence, the equation of the directrix are $x=\pm \frac{25}{4}$