Find the equation of the ellipse whose major axis is 8 and co-ordinates of foci are `(pm2,0)`

Explanation

The foci of the ellipse are on x-axis.
`:." "agtb`
Major axis =2a and foci `=(pmae,0)`
`:." "2a=8" "rArr" "a=4`
and ae=2
`rArr" "e=(2)/(4)=(1)/(2)`
Now `b^(2)=a^(2)(1-e^(2))`
`=16(1-(1)/(4))=12`
Therefore, the equation of ellipse
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
`rArr" "(x^(2))/(16)+(y^(2))/(12)=1`
`rArr" "3x^(2)+4y^(2)=48`.