Question

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

• A. 3y = 5
• B. y = 5
• C. 3y = 25
• D. y = 3

Answer 1

Answer: (C)

3y = 25

Answer 2

Equation of ellipse $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1$ , where a > b
Given, $\frac{x^{2}}{16} + \frac{y^{2}}{75} = 1 \Rightarrow b = 4 , a=5$
But $e=\sqrt{1 - \frac{b^{2}}{a^{2}}} = \sqrt{1 -\frac{16}{25}}$
$\Rightarrow e = \frac{3}{5}$
$\therefore$ equation of directrix $y = \pm \frac{a}{e}$
$\therefore y = \pm \frac{5}{\frac{3}{5}} \Rightarrow 3y = \pm 25$