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ABCD is a rhombus with AC=2BD. Diagonal...

ABCD is a rhombus with AC=2BD. Diagonals AC and BD intersect at `P.E_(1),E_(2),E_(3) and E_(4)` are four ellipes passing through P and their foci are A and B, B and C, C and D and D and A, respectively . If for `i=1,2,3,4,e_(i)` are the eccentricities fo `E_(i)`, then

A

`e_(i)=e_(3)`

B

`e_(2)=e_(4)`

C

`e_(1)=2e_(2)`

D

`e_(1)=e_(2)`

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the properties of the rhombus ABCD and the ellipses defined by the points A, B, C, D, and the intersection point P of the diagonals AC and BD. ### Step-by-Step Solution: 1. **Understanding the Rhombus and its Diagonals**: - Let the diagonals AC and BD intersect at point P. - Given that AC = 2BD, we can denote the lengths as follows: - Let BD = 2x, then AC = 4x. ...
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