Question

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 `16x^(2)+y^(2)=16`

Answer 1

`16x^(2)+y^(2)=16`
`rArr" "(x^(2))/(1)+(y^(2))/(16)=1`
Comparing with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
Here, `a^(2)=1,b^(2)=16" "rArr" "a=1,b=4`
`:.altb`.
The major axis of ellipse will be along y-axis.
Vertices `-=(0,pmb)-=(0,pm4)`
Major axis =2b=8,
Minor axis =2a=2
Eccentricity `e=sqrt(1-(a^(2))/(b^(2)))=sqrt(1-(1)/(16))=(sqrt(15))/(4)`
Coordinates of foci `-=(0,pmbe)-=(0,pmsqrt(15))`
Length of latus rectum `=(2a^(2))/(b)=(2xx1)/(4)=(1)/(2)`