1.

ABCD isa 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 andB, 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

Answer»

`e_(i)=e_(3)`
`e_(2)=e_(4)`
`e_(1)=2e_(2)`
`e_(1)=e_(2)`

SOLUTION :
AB=BC=CD=DA=
Since `DeltaPAB, DeltaPBC, DeltaPCD, DeltaPDA` are congruent,
`e_(1)=e_(2)=e_(3)=3_(4)=(a)/(PA+PB)`


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