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Let E1 and E2, be two ellipses whose cen...

Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle `x^2 + (y-1)^2= 2`. The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that `PQ=PR=[2sqrt2]/3`.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):

A

(a)`e_1^(2)+e_2^(2)=43/40`

B

(b)`e_1e_2=sqrt7/(2sqrt10)`

C

(c)`abs e_1^(2)-e_2^(2)|=5/8`

D

(d)`e_1e^(2)=sqrt3/4`

Text Solution

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The correct Answer is:
A, B
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