SATHEE: Hyperbola 1 Question 8

Hyperbola 1 Question 8

9. The eccentricity of the hyperbola whose length of the latusrectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is

(a) $\frac{4}{3}$

(b) $\frac{4}{\sqrt{3}}$

(d) $\sqrt{3}$

(2017 Main)

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Answer:

Correct Answer: 9. $16 x^{2} + y^{2} + 10 x y = 2$

Solution:

We have, $\frac{2 b^{2}}{a} = 8$ and $2 b = a e$

$\Rightarrow b^{2} = 4 a$ and $2 b = a e$

Consider,

$\begin{aligned} 2 b & = a e \\ 4 b^{2} & = a^{2} e^{2} \end{aligned}$

$\begin{aligned} \Rightarrow & 4 a^{2} (e^{2} - 1) & = a^{2} e^{2} \\ \Rightarrow & 4 e^{2} - 4 & = e^{2} \\ \Rightarrow & 3 e^{2} & = 4 \\ \Rightarrow & e & = \frac{2}{\sqrt{3}} \end{aligned}$

$[∵ a \neq 0]$

$[∵ e > 0]$

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Hyperbola 1 Question 8

9. The eccentricity of the hyperbola whose length of the latusrectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, 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

Hyperbola 1 Question 8

9. The eccentricity of the hyperbola whose length of the latusrectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, 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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