Gujarat BoardEnglish MediumSTD 11 ScienceMATHSHyperbola1 Mark
Question
Write the distance between the directrices of the hyperbola $\text{x}=8\sec\theta,\ \text{y}=8\tan\theta.$
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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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