Question

Find the equation of the ellipse (referred to its axes as the axes of `xa n dy` , respectively) whose foci are `(+-2,0)` and eccentricity is `1/2`

Answer 1

Let the ellipse be `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
Given`e=(1)/(2)`
Also, foci of ellipse are `(+-ae,0)-=(+-2,0)`
`rArr ae=2 rArr a=4`
Now, `b^(2)=a^(2)(1-e^(2)) rArr b^(2) =12`
Therefore, equation of ellipse is `(x^(2))/(16)+(y^(2))/(12)=1`