`4x^(2)+9y^(2)=36rArr(x^(2))/(9)+(y^(2))/(4)=1`
Comparing with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`:.a^(2)=9" "rArr" "a=3`
`b^(2)=4" "rArr" "b=2`
Here, `agtb`.
`:.` The major axis of ellipse will be along x-axis. Now, vertices `-=(pma,0)-=(pm3,0)`
Eccentricity `e=sqrt(1-(b^(2))/(a^(2)))=sqrt(1-(4)/(9))=sqrt((5)/(9))=(sqrt(5))/(3)`
Now `ae=3xx(sqrt(5))/(3)=sqrt(5)`
`:.` Coordinates of foci `-=(ae,0) -=(pmsqrt(5),0)`
Major axis `=2a=2xx3=6`
Minor axis `=2b=2xx2=4`
Length of latus rectum `=(2b^(2))/(a)=(2xx4)/(3)=(8)/(3)`