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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