Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.`(x^2)/(36)+(y^2)/(16)=1`

Explanation

Equation of ellipse : `(x^(2))/(36)+(y^(2))/(16)=1`
Comparing with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`:." "a^(2)=36andb_(2)=16`
`rArr" "a=6andb=4`
`"Here",agtb`.
`:.` Major axis of the ellipse will along x-axis.
Vertices `-=(pma,0)-=(pm6,0)`
Eccentricity `e=sqrt(1-(b^(2))/(a^(2)))=sqrt(1-(16)/(36))=sqrt((20)/(36))`
`rArr" "e=(sqrt(5))/(3)`
coordinates of foci `-=(pmae,0)`
`-=(pm6xx(sqrt(5))/(3),0)-=(pm2sqrt(5,)0)`
Major axis `=2a2xx6=12`
Minor axis `=2b=2xx4=8`
Length of latus rectum `=(2b^(2))/(a)=(2xx16)/(6)=(16)/(3)`