If the foci of an ellipse are `(0,+-1)` and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.

Answer

`20x^(2)+4y^(2)=5`

Explanation

Let the ellipse be
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (altb)=1`
Since the foci are, `(0+-1)`,
be =1 and 2a=1 `" "` [ Since minor axis is of length 1]
Also,` a^(2)=b^(2)(1-e^(2))`
or `(1)/(4)=b^(2)-b^(2)e^(2)=b^(2)-1`
or `b^(2)=1+(1)/(4)=(5)/(4)`
Hence oof the equation of the ellipseis
`(x^(2))/(1//4)+(y^(2))/(5//4)=1 or 20x^(2)+4y^(2)=5`