Find the equation of the ellipse whose centre is at origin, the distance between foci is `2` and eccentricity is `(1)/(sqrt(2))`.

Explanation

Let the equation of the ellipse be `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and agtb`.
Here `e=(1)/(sqrt(2))` and the distance between foci = 2ae = 2
`rArr" "ae=1`
`rArr" "a((1)/(sqrt(2)))=1`
`rArr""a=sqrt(2)`
`rArr" "a^(2)=2`
and `b^(2)=a^(2)(1-e^(2))`
`=a^(2)-(a^(2)e^(2))=2-1=1`
`:.` Equation of ellipse
`(x^(2))/(2)+(y^(2))/(1)=1`
`rArr" "x^(2)+2y^(2)=2`.