​ Let E1 : x^2/a^2 + y^2/b^2 = 1, a > b. Let E2 be another ellipse such that it touches the end points of major axis of E1 and the foci of E2

Question

Let E₁ : \(\frac{x^2}{a^2}+\frac{y^2}{b^2}\) = 1, a > b. Let E₂ be another ellipse such that it touches the end points of major axis of E₁ and the foci of E₂ are the end points of minor axis of E₁. If E₁ and E₂ have same eccentricities, then its value is :

(1) -1+√5/2

(2) -1+√8/2

(3) -1+√3/2

(4) -1+√6/2

Answer 1

Answer is: (1) -1+√5/2

Also b = ce