The length of the major axis of an ellipse is 20 units, and its foci are . Find the equation of the ellipse.


Let the equation of the required ellipse be



Given: Length of Major Axis = 20units …(i)


We know that,


Length of Major Axis = 2a …(ii)


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


2a = 20


a = 10


It is also given that,


Coordinates of foci = (±5√3, 0) …(iii)


We know that,


Coordinates of foci = (±c, 0) …(iv)


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


c = 5√3


We know that,


c2 = a2 – b2


(5√3)2 = (10)2 – b2


75 = 100 – b2


b2 = 100 – 75


b2 = 25


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




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