Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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# Find the Equation of the Hyperbola, Referred to Its Principal Axes as Axes of Coordinates, In the Conjugate Axis is 5 and the Distance Between Foci = 13 . - Mathematics

Answer in Brief

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in  the  conjugate axis is 5 and the distance between foci = 13 .

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#### Solution

The distance between the foci is $2ae$ .

$\therefore 2ae = 13$

$\Rightarrow ae = \frac{13}{2}$

Length of the conjugate axis,

$2b = 5$

$\Rightarrow b = \frac{5}{2}$

Also, $b^2 = a^2 ( e^2 - 1)$

$\Rightarrow \left( \frac{5}{2} \right)^2 = \left( \frac{13}{2} \right)^2 - a^2$

$\Rightarrow a^2 = \frac{169 - 25}{4}$

$\Rightarrow a^2 = \frac{144}{4} = 36$

$\Rightarrow a = 6$

Therefore, the standard form of the hyperbola is $\frac{x^2}{36} - \frac{4 y^2}{25} = 1$ .

$or 25 x^2 - 144 y^2 = 900$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 27 Hyperbola
Exercise 27.1 | Q 6.2 | Page 13
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