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Hyperbola — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsHyperbola1 Mark
Question
Write the distance between the directrices of the hyperbola $\text{x}=8\sec\theta,\ \text{y}=8\tan\theta.$
✓

Answer

We have:
$\text{x}=8\sec\theta,\ \text{y}=8\tan\theta$
On squaring and subtracting, we get:
$\text{x}^2-\text{y}^2=64\sec^2\theta-64\tan^2\theta$
$\Rightarrow\ \text{x}^2-\text{y}^2=64$
$\Rightarrow\ \frac{\text{x}^2}{64}-\frac{\text{y}^2}{64}=1$
$\therefore$ a = b = 8
Distance between the directrices of hyperbola is $\frac{2\text{a}^2}{\sqrt{\text{a}^2+\text{b}^2}}.$
$\Rightarrow\ \frac{2\times64}{\sqrt{64+64}}$
$=\ \frac{128}{8\sqrt2}$
$=\frac{16}{\sqrt2}$
$=8\sqrt2$

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