Let E 1 : x 2 a 2 + y 2 b 2 = 1 , a > b . Let E 2 be another ellipse such that it touches the end points of major axis of E 1 and the foci of E 2 are the end points of minor axis of E 1 . If E 1 and E 2 have same eccentricities, then it

Question

Let E 1 : x 2 a 2 + y 2 b 2 = 1 , a &#62; b . Let E 2 be another ellipse such that it touches the end points of major axis of E 1 and the foci of E 2 are the end points of minor axis of E 1 . If E 1 and E 2 have same eccentricities, then its value is:

Quantrex Academy · Accepted Answer

Correct answer: A. - 1 + 5 2

Given ellipse is E 1 : x 2 a 2 + y 2 b 2 = 1 , &#160; a &#62; b and E 2 is another ellipse which touches the end points of the major axis of E 1 and foci of E 2 are at the minor axis of E 1 , thus the two ellipses are given by the following diagram. Since, the ellipse E 2 touches the major axis of the ellipse E 1 , hence, the minor axis of the ellipse E 2 is a 1 = a . Now, let the major axis of the ellipse E 2 is b 1 = c and it is obvious from the diagram and the given conditions that b 1 &#62; a 1 . We know that t

Let E 1 : x 2 a 2 + y 2 b 2 = 1 , a > b . Let E 2 be another ellipse such that it touches the end points of major axis of E 1 and the foci of E 2 are the end points of minor axis of E 1 . If E 1 and E 2 have same eccentricities, then its value is:

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Correct answer

Step-by-step solution

More from Ellipse

Let E 1 : x 2 a 2 + y 2 b 2 = 1 , a &#62; b . Let E 2 be another ellipse such that it touches the end points of major axis of E 1 and the foci of E 2 are the end points of minor axis of E 1 . If E 1 and E 2 have same eccentricities, then its value is:

Options

Correct answer

Step-by-step solution

More from Ellipse

Let E 1 : x 2 a 2 + y 2 b 2 = 1 , a > b . Let E 2 be another ellipse such that it touches the end points of major axis of E 1 and the foci of E 2 are the end points of minor axis of E 1 . If E 1 and E 2 have same eccentricities, then its value is: