Question

For hyperbola $-\frac{x^2}{16}+\frac{y^2}{25}=1$ distance between directrices is

• A. $\frac{50}{\sqrt{41}}$
• B. $\frac{16}{\sqrt{41}}$
• C. $\frac{25}{\sqrt{41}}$
• D. $\frac{32}{\sqrt{41}}$

Answer 1

The correct option is A $\frac{50}{\sqrt{41}}$

Given equation is $-\frac{x^2}{16}+\frac{y^2}{25}=1$

$\Rightarrow \frac{y^2}{25}-\frac{x^2}{16}=1$

Distance between directrix is $\frac{2a}{\sqrt{a^2+b^2}}$

Here $a=25,b=16$

So, answer is $=\frac{50}{\sqrt{41}}$.