Let E1 and E2 be two ellipses whose centers are in origin. The major axes of E1 and E2 lies along the x−axis and y−axis, respectively. Let S be the circle x2+(y−1)2=2.. The straight lin x+y=3 touches the curves S, E1 and E2 at P,Q and R, respectively. Supoose the PQ=PR=2√23.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are)

Let E1 and E2 be two ellipses whose centers are in origin. The major a

1.	Let E1 and E2 be two ellipses whose centers are in origin. The major axes of E1 and E2 lies along the x−axis and y−axis, respectively. Let S be the circle x2+(y−1)2=2.. The straight lin x+y=3 touches the curves S, E1 and E2 at P,Q and R, respectively. Supoose the PQ=PR=2√23.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are)
Answer» Let $E_{1}$ and $E_{2}$ be two ellipses whose centers are in origin. The major axes of $E_{1}$ and $E_{2}$ lies along the $x -$ axis and $y -$ axis, respectively. Let $S$ be the circle $x^{2} + (y - 1)^{2} = 2.$ . The straight lin $x + y = 3$ touches the curves $S$ , $E_{1}$ and $E_{2}$ at $P, Q$ and $R,$ respectively. Supoose the $P Q = P R = \frac{2 \sqrt{2}}{3} .$ If $e_{1}$ and $e_{2}$ are the eccentricities of $E_{1}$ and $E_{2}$ , respectively, then the correct expression(s) is(are)