JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q82

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MathematicsSingle correct+4 / -1Question 82 of 90

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 :

\dfrac43

\dfrac4{\sqrt3}

\dfrac2{\sqrt3}

\sqrt3

Answer and worked solution

Official answer: C

$\frac{2b^2}a=8$ and $2b=\frac12(2ae)$ , so $b=\frac{ae}2$ . With $b^2=a^2(e^2-1)$ : $\frac{e^2}4=e^2-1$ , so $e=\frac2{\sqrt3}$ .

Topics:Hyperbola

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 82