Question

For hyperbola $\frac{x^2}{16}-\frac{y^2}{25}=1$ distances between two directrices are

• A. $\frac{16}{\sqrt{41}}$
• B. $\frac{25}{\sqrt{41}}$
• C. $\pm \frac{32}{\sqrt{141}}$
• D. $\frac{32}{\sqrt{41}}$

Answer 1

The correct option is D $\frac{32}{\sqrt{41}}$

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

Here $a^2=16,b^2=25$

Distance between directrix is $\frac{2a^2}{\sqrt{a^2+b^2}}=\frac{2\times 16}{\sqrt{16+25}}=\frac{32}{\sqrt{41}}$