Q24 of 26 Page 756

Find the equation of an ellipse whose eccentricity is , the latus rectum is 5, and the center is at the origin.


Let the equation of the required ellipse is


…(i)


Given that



we know that,





We know that,


c2 = a2 – b2






…(ii)


It is also given that, Latus Rectum = 5 …(iii)


We know that,









Substituting the value of a in eq. (ii), we get





Substituting the value of a2 and b2 in eq. (i), we get




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