JEE Main 2017 · Mathematics · Conic Sections · easy

The length of the latus rectum of the ellipse (x^2/(25)+(y^2/(16)=1 is

Single correct option

The length of the latus rectum of the ellipse

\dfrac{x^2}{25}+\dfrac{y^2}{16}=1

Show answer and solution

Answer: (A) $\dfrac{32}{5}$

Here

a^2=25

and

b^2=16

, so

a=5

and

b=4

with

a>b

. The latus rectum has length

\dfrac{2b^2}{a}=\dfrac{2\cdot16}{5}=\dfrac{32}{5}

. The option

16/5

forgets the factor 2 and

25/4

uses

2a^2/b

with the axes interchanged.

Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake