Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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# Write the Distance Between the Directrices of the Hyperbola X = 8 Sec θ, Y = 8 Tan θ. - Mathematics

Answer in Brief

Write the distance between the directrices of the hyperbola x = 8 sec θ, y = 8 tan θ.

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#### Solution

We have: $x = 8\sec\theta, y = 8\tan\theta$

On squaring and subtracting, we get:

$x^2 - y^2 = 64 \sec^2 \theta - 64 \tan^2 \theta$

$\Rightarrow x^2 - y^2 = 64$

$\Rightarrow \frac{x^2}{64} - \frac{y^2}{64} = 1$

∴ a = b = 8
Distance between the directrices of  hyperbola is $\frac{2 a^2}{\sqrt{a^2 + b^2}}$.

$\Rightarrow \frac{2 \times 64}{\sqrt{64 + 64}}$

$= \frac{128}{8\sqrt{2}}$

$= \frac{16}{\sqrt{2}}$

$= 8\sqrt{2}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 27 Hyperbola
Q 8 | Page 18
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