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))/(16)+(y^(2))/(9)=1`

Answer» `(x^(2))/(16)+(y^(2))/(9)=1`
`:.` Comparing with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`:.a^(2)=16" "rArr" "a=4`
`b^(2)=9" "rArr" "b=3`
`:." "agtb`.
The major aixs of the ellipse will be along x-axis.
Vertices `-=(pma,0)-=(pm4,0)`
Major axis = ab = 2(3) = 6
Eccentricity `e=sqrt(1-(b^(2))/(a^(2)))=sqrt(1-(1)/(16))=(sqrt(7))/(4)`
coordinates of foci `-=(pmae,0)-=(pmsqrt(7),0)`
Latus rectum `=(2b^(2))/(a)=(2xx9)/(4)=(9)/(2)`


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