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):

Options

A. `e_1^2+e_2^2 = 43/40`
B. `e_1e_2 =sqrt7/2sqrt10`
C. `|e_1^2+e_2^2| =5/8`
D. `e_1e_2 = sqrt3/4`

Answer

A, B