Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Find the Equation of the Hyperbola Satisfying the Given Condition : Foci (± 3 √ 5 0), the Latus-rectum = 8 - Mathematics

Find the equation of the hyperbola satisfying the given condition :

 foci (± \[3\sqrt{5}\] 0), the latus-rectum = 8

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Solution

 The foci of  the hyperbola  are \[\left( \pm 5, 0 \right)\] and the transverse axis is 8.
Thus, the value of  \[ae = 5\] and 2a = 8.

\[\Rightarrow a = 4\]

Now, using the relation

\[b^2 = a^2 ( e^2 - 1)\], we get:

\[\Rightarrow  b^2  = 25 - 16\] 
 
\[ \Rightarrow  b^2  = 9\] 
Thus, the equation of the hyperbola is \[\frac{x^2}{16} - \frac{y^2}{9} = 1\].
  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 27 Hyperbola
Exercise 27.1 | Q 11.04 | Page 14
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