Question

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

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

Answer 1

Answer: (A)

$y = \frac{25}{3}$

Answer 2

From the given equation of ellipse $a^{2} = 16,b^{2} = 25$ (since $b > a$)

So, $a^{2} = b^{2}(1 - e^{2})$ , ∴ $16 = 25(1 - e^{2})$

$\Rightarrow 1 - e^{2} = \frac{16}{25} \Rightarrow e^{2} = \frac{9}{25}$ ⇒ $e = \frac{3}{5}$

∴ One directrix is $y = \frac{b}{e} = \frac{5}{3/5} = \frac{25}{3}$