IIT JEE Main 2016 Maths Question 38:

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:

(1) 2/√3 |

(2) √3 |

(3) 4/3 |

(4) 4/√3 |

#### Solution

Given in problem statement that for the hyperbola whose length of the latus rectum is equal to 8, i.e.

2b^{2}/a=8

& the length of its conjugate axis is equal to half of the distance between its foci, hence, 2b =ae

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

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

=> e = 2/√3

#### Answer to IIT JEE Main 2016 Maths Question 38

Correct answer to given problem No 38 of IIT JEE Main Maths paper of 2016 is option number (1) that is the eccentricity of hyperbola is 2/√3.