Conic Sections — MATHS STD 11 Science — Question

1. $8\sqrt2$

Solution:

We have:

$\text{x}=8\sec\theta,\text{y}=8\tan\theta$

On squaring and subtracting:

$\text{x}^2-\text{y}^2=8\sec^2\theta-8\tan^2\theta$

$\Rightarrow\text{x}^2-\text{y}^2=8$

$\Rightarrow\frac{\text{x}^2}{8}-\frac{\text{y}^2}{8}=1$

$\therefore\text{a}=\text{b}=\text{c}$

Distance between the directrices of the hyperbola $=\frac{2\text{a}^2}{\sqrt{\text{a}^2+\text{b}^2}}$

Distance between the directrices $=\frac{2\times64}{\sqrt{64+64}}$

$=\frac{128}{8\sqrt2}$

$=\frac{16}{\sqrt2}$

$=8\sqrt2$