Find the equation of the ellipse whose vertices are the (0, ±4) and foci at .


Given: Vertices = (0, ±4) …(i)


The vertices are of the form = (0, ±a) …(ii)


Hence, the major axis is along y – axis


From eq. (i) and (ii), we get


a = 4


a2 = 16


and We know that, if the major axis is along y – axis then the equation of Ellipse is of the form of



Also, given coordinate of foci = (0, ±√7) …(iii)


We know that,


Coordinates of foci = (0, ±c) …(iv)


From eq. (iii) and (iv), we get


c = √7


We know that,


c2 = a2 – b2


(√7)2 = (4)2 – b2


7 = 16 – b2


b2 = 16 – 7


b2 = 9


Substituting the value of a2 and b2 in the equation of an ellipse, we get




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