QJEEM16Ma3690: JEE Main 2016 Mathematics - Class 11 JEEM16Ma3690 Solution: The eccentricity of the hyperbola whose length of the latus…

Question

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The eccentricity of the hyperbola whose length of the latus rectum is equal to

8

and the length of its conjugate axis is equal to half of the distance between its foci, is :

Accepted Answer

\frac{2 b^{2}}{a} = 8

and

2 b = \frac{1}{2} (2 a e)

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

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

\Rightarrow 3 e^{2} = 4 \Rightarrow e = \frac{2}{\sqrt{3}}

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