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)

Show Answer

Answer:

Correct Answer: 9. (c)

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,

$2 b = a e$

$4 b^{2} = a^{2} e^{2}$

$\Rightarrow 4 a^{2} (e^{2} - 1) = a^{2} e^{2}$

$\Rightarrow 4 e^{2} - 4 = e^{2}$ $[∵ a \neq 0]$

$\Rightarrow 3 e^{2} = 4$

$\Rightarrow e = \frac{2}{\sqrt{3}}$ $[∵ e > 0]$

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Hyperbola 1 Question 8

9.

Answer:

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