Home
Class 12
MATHS
If the latus rectum of an ellipse is equ...

If the latus rectum of an ellipse is equal to the half of minor axis, then find its eccentricity.

A

`1/2`

B

`sqrt3/2`

C

`3/4`

D

`sqrt(15)/4`

Text Solution

Verified by Experts

The correct Answer is:
B
Length of latus rectum of an ellipse is `(2b^(2))/a` whereb is semi minor axis. As given , `(2b^(2))/a=b`
`rArr" "2b=arArrb/a=1/2`
`"We know that occentricitye "=sqrt(1-b^(2)/a^(2))=sqrt(1-1/4)=sqrt3/2`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS

    NDA PREVIOUS YEARS|Exercise Multiple choice question|109 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    NDA PREVIOUS YEARS|Exercise DIRECTIONS|60 Videos

Similar Questions

Explore conceptually related problems

If the latursrectum of an ellipse is equal to half of its minor-axis, then find its eccentricity.

If the latusrectum of an ellipse is equal to half of minor axis,find its eccentricity.

Knowledge Check

  • If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity ?

    A
    `2/sqrt3`
    B
    `1/sqrt3`
    C
    `sqrt3/2`
    D
    `1/sqrt2`

  • If the latus rectum of an ellipse is equal to one half it minor axis, what is the eccentricity of the ellipse?

    A
    `(1)/(2)`
    B
    `(sqrt(3))/(2)`
    C
    `(3)/(4)`
    D
    `(sqrt(15))/(4)`

  • If the latusrectum of an ellipse is equal to one half of its minor axis , then eccentricity is equal to

    A
    `(1)/(sqrt(2))`
    B
    `(sqrt(3))/(2)`
    C
    `(1)/(2)`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    If the distance between the foci of an ellipse is equal to length of minor axis, then its eccentricity is

    If the distance between the foci of an ellipse is equal to its minor axis, then eccentricity e of the ellipse is :

    If the normal at an end of a latus rectaum of an ellipse passes through an extremity of the minor axis then the eccentricity of the ellispe satisfies .

    The latus rectum of an ellipse is half of its minor axis. Its eccentricity is :

    The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be

    Home
    Profile