Find the equation of the ellipse in each of the cases given below :
(i) foci `( -+ 3, 0) ,e = 1/2`
(ii) foci ` ( 0, -+ 4)` and end points of major axis are `( 0 -+ 5)`
(iii) length of lagtus rectum 8, eccentricity ` = 3/5` and major axis on x-axis .
(iv) length of latus rectum 4, distance between foci ` 4sqrt2` and major axis as y -axis.

Answer

(i) ` x^(2)/36 + y^(2) /27 = 1`
(ii) ` a^(2) =9`
(iii) ` (16 x^(2))/(625) + y^(2)/25 =1`
(iv) ` x^(2)/8 + y^(2)/16 =1`