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)

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 $y=\pm \frac{a}{e}$
$\therefore y=\pm \frac{5}{\frac{3}{5}}\Rightarrow 3y=\pm 25$