Question

If the latusrectum of an ellipse is equal to half of minor axis, find its eccentricity.
A. `1/2`
B. `sqrt3`
C. `sqrt3//2`
D. `1/sqrt2`

Answer 1

Correct Answer - C
Let the equation of ellipse be `x^(2)/a^(2)+y^(2)/b^(2)=1`
`"Length of minor axis = 2b"`
`" and length of latus rectum "=(2b^(2))/a`
According to the equation,
`(2b^(2))/a=brArr2b=arArr4b^(2)=a^(2)`
Now, eccentricity of ellipse
`e=sqrt(a^(2)-b^(2))/a`
`e=sqrt(4b^(2)-b^(2))/(2b)=(sqrt3b)/(2b)=sqrt3/2`
`rArr" "e=sqrt3/2`