Questions

ABCD is a rhombus with AC = 2BD. Diagonals AC and BD intersect at P. E_{1}, E_{2}, E_{3} and E_{4} arc four ellipses 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 of E_{i} then

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a

e1 = e3

b

e2 = e4

c

e1 = 2e2

d

e1 = e2

detailed solution

Correct option is A

AB = BC = CD = DA = aSince, ΔPAB,△PBC,ΔPCD,△PDA are congruent,e1=e2=e3=e4=aPA+PB

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