SATHEE: Hyperbola 1 Question 4

Hyperbola 1 Question 4

5. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 , then the eccentricity of the hyperbola is

(2019 Main, 11 Jan II)

(a) $\frac{13}{12}$

(b) 2

(d) $\frac{13}{6}$

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Answer:

Correct Answer: 5. (b)

Solution:

We know that in $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ , where $b^{2} = a^{2} (e^{2} - 1)$ , the length of conjugate axis is $2 b$ and distance between the foci is 2 ae.

$∴$ According the problem, $2 b = 5$ and $2 a e = 13$

Now,

$b^{2} = a^{2} (e^{2} - 1)$

$\Rightarrow \frac{5}{2}^{2} = a^{2} e^{2} - a^{2}$

$\Rightarrow \frac{25}{4} = \frac{(2 a e)^{2}}{4} - a^{2}$

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

$[∵ 2 a e = 13]$

$\Rightarrow a^{2} = \frac{169 - 25}{4} = \frac{144}{4} = 36$

$\Rightarrow a = 6$

Now, $2 a e = 13$

$\Rightarrow 2 \times 6 \times e = 13$

$\Rightarrow e = \frac{13}{12}$

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Hyperbola 1 Question 4

5. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 , then the eccentricity of the hyperbola is

Answer:

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Hyperbola 1 Question 4

5. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 , then the eccentricity of the hyperbola is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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