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))/(25)+(y^(2))/(100)=1`

Explanation

`(x^(2))/(25)+(y^(2))/(100)=1`
Comparing with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`a^(2)=25" "rArr" "a=5`
`b^(2)=100" "rArr" "b=10`
Here, `agtb`.
`:.` The major axis of the ellipse will be along the y-axis.
Vertices `-=(0,pmb)-=(0,pm10)`
Eccentricity `e=sqrt(1-(a^(2))/(b^(2)))=sqrt(1-(25)/(100))=(3)/(4)`
`rArr" "e=(sqrt(3))/(2)`
`:." "be=10xx(sqrt(3))/(2)=5sqrt(3)`
Coordinates of foci `-=(0,pmbe)-=(0,pm5sqrt(3))`
Major axis `=2b=2xx10=20`
Minor axis `=2a=2xx5=10`
Length of latus rectum `=(2a^(2))/(b)=(2xx25)/(10)=5`