Find the equation of the ellipse having minor axis of length 1 and foci (0,1), (0,-1). Also find its latus rectum.

Explanation

Since foci are on y-axis we consider equations of ellipse as `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1,altb`
Given foci are `(o,+-be)-=(0,+-1)`
`:. Be =1`
Length of minor axis is 2a
So, `2a=1 rAr a=(1)/(2)`
Now, `a^(2)=b^(2)(1-e^(2))`
`rArr (1)/(4)=b^(2)-b^(2)e^(2)=b^(2)-1`
`rArr b^(2)=(5)/(4)`
So, the equation of ellipse is `(x^(2))/(1//4)+(y^(2))/(5//4)=1 or 4x^(2)+(4y^(2))/(5)=1`