Home
Class 12
MATHS
If the line joining foci subtends an ang...

If the line joining foci subtends an angle of `90^(@)` at an extremity of minor axis, then the eccentricity e is

A

`(1)/(sqrt(6))`

B

`(1)/(sqrt(3))`

C

`(1)/(sqrt(2))`

D

`(1)/(2sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
C

`:.F_(1)B bot F_(2)B`
`rArr m_(1)m_(2)= -1`
`rArr (b-0)/(0-ae) xx (b-0)/(0+a e) = -1`
`rArr (b^(2))/(a^(2)e^(2))=1`
`rArr 2e^(2)=1`
`rArr e^(2)=(1)/(2)`
`rArr e=(1)/(sqrt(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the angle between the lines joining the foci of any ellipse to an extremity of the minor axis is 90^0 , find the eccentricity. Also find the equation of the ellipse if the major axis is 2sqrt(2) .

If the angle between the lines joining the foce of any ellipse to an extremity of the minor axis is 90^0 , find the accentricity. Find also the equation of the ellipse if the major axis is 2sqrt(2) .

If the minor axis of an ellipse subtends an angle of 60^(@) at each focus of the ellipse, then its eccentricity, is

If the lines joining the foci of an ellipse to an end of its minor axis are at right angles , then the eccentricity of the ellipse is e =

If latus-rectum is one-third minor axis, then eccentricity of the ellipse is

If the angle between the lines joining the Foci to an extremity of minor axis of an ellipse is " 90^(@). " Its eccentricity is ' e ' then " 8e^(2) " 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 line joining the foci F and F' of an ellipse subtend a right angle at the positive end B of the minor axis.If e is the eccentricity of the ellipse then the value of 2e^(2)+1 is equal to

In an ellipse,if the lines joining focus to the extremities of the minor axis form an equilateral triangle with the minor axis,then the eccentricity of the ellipse is