1.

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))/(100)+(y^(2))/(400)=1`

Answer» `(x^(2))/(100)+(y^(2))/(400)=1`
Comparing with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`:.a^(2)=100" "rArr" "a=10`
`b^(2)=400" "rArr" "b=20`
Here, `altb`.
`:.` the major axis of the ellipse wil be along y-axis.
Vertices `-=(0,pmb)-=(0,pm20)`
Eccentricity `e=sqrt(1-(a^(2))/(b^(2)))=sqrt(1-(100)/(400))=sqrt((3)/(4))=(sqrt(3))/(2)`
Now, be `=20xx(sqrt(3))/(2)xx10sqrt(3)`
`:. "Coordinates of foci" -=(0,pmbe)-=(0,pm10sqrt(3))`
Major axis `=2b=2xx20=40`
Minor axis `=2a=2xx10=20`
Length of latus rectum `=(2a^(2))/(b)=(2xx100)/(20)=10`


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