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Let E ₁: x^2 9 + y^2 4 =1 be an ellipse. Ellipses E ₁ 's are constructed such that their centres and eccentricities are same as that of E₁ , and the length of minor axis of E_i is the length of major axis of E_ i+1 (i 1) . If A_i is the area of the ellipse E_i , then 5 ( _ i=1 ^ A_i ) , is equal to

Correct answer

0

Step-by-step solution

aligned & E ₁= x ^2 9 + y ^2 4 e = 1- 4 9 = 5 3 & E ₂: x ^2 a ^2 + y ^2 4 =1 & e = 5 3 = 1- a ^2 4 5 9 =1- a ^2 4 & a ^2= 16 9 aligned aligned & E ₂: x ^2 16 9 + y ^2 4 =1 & E ₃: x ^2 16 9 + y ^2 ~b ^2 =1 & e = 5 3 = 1- b ^2 16 9 b^2= 64 81 aligned aligned & E ₃= x ^2 16 9 + y ^2 64 81 =1 & ~A ₁= 3 2 6 & ~A ₂= 4 3 2= 8 3 & ~A ₃= 4 3 8 9 = 32 81 & _ i =1 ^ A _ i =6 + 8 3 + 32 81 + . 6 1- 4 9 54 5 & 5 _ i =1 ^ A _ i 5 54 5 =54 aligned

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