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Answer:
The foci of the given ellipse = (0 ,-√5 ) and ( 0, √5 )
Step-by-step explanation:
Step(i):-
Given Ellipse 9 x² + 4 y² = 36
[tex]\frac{9x^{2} }{36} + \frac{4y^{2} }{36} =1[/tex]
⇒ [tex]\frac{x^{2} }{4} + \frac{y^{2} }{9} = 1[/tex]
Step(ii):-
The Major axis lies on y-axis
Foci of the Formula C² = a² -b² = 9-4 =5
C = √5
The Foci is always lie on the major axis(longest) axis, spaced equally each side of the centre
Given ellipse of the foci is lie on Y- axis
Final answer:-
The foci of the given ellipse = (0 ,-√5 ) and ( 0, √5 )