`36x^(2)+4y^(2)=144`
`rArr(x^(2))/(4)+(y^(2))/(36)=1`
Comparing with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`:.a^(2)=4" "rArr" "a=2`
`b^(2)=36" "rArr" "b=6`
Here, `altb`.
`:.` The major axis of the ellipse will be along y-axis.
Vertices `-=(0,pmb)-=(0,pm6)`
Eccentricity `e=sqrt(1-(a^(2))/(b^(2)))=sqrt(1-(4)/(36))=(2sqrt(2))/(3)`
`:.be=6xx(2sqrt(2))/(3)=4sqrt(2)`
Now coordinates of foci `-=(0,pmbe)-=(0,pm4sqrt(2))`
Major `=2b=2xx6=12`
Minor axis `=2a=2xx2=4`
Length of latus rectum `=(2a^(2))/(b)=(2xx4)/(6)=(4)/(3)`