If the length of the major axis of the ellipse `((x^(2))/(a^(2)))+((y^(2))/(b^(2)))=1` is three times the length of minor axis, its accentricity is

Options

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

Answer

D

Explanation

`because2a=3*2*bimpliesa=3b`
`therefore e=sqrt((a^(2)-b^(2))/(a^(2)))=sqrt(((3b)^(2)-b^(2))/((3b)^(2)))`
`=sqrt((8b^(2))/(9b^(2)))=(2sqrt(2))/(3)`