Given that focus is (0,5√3)⇒|b|>|a| Let b>a>0 and foci is (0,±be) ∵a2=b2−b2e2⇒b2e2=b2−a2 be=√b2−a2⇒b2−a2=75 . . . . (i) ∵2b−2a=10⇒b−a=5 . . . . (ii) From (i) and (ii) b+a=15 . . . . (iii) On solving (ii) and (iii), we get ⇒b=10,a=5 Now, length of latus rectum =