Let E1 and E2 be two ellipse whose centres are at the origin. The major axes of E1 and E2 lie along x-axis and y-axis respectively. Let S be the circle x2+(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=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 ellipse whose centres are at the origin. The majo

1.	Let E1 and E2 be two ellipse whose centres are at the origin. The major axes of E1 and E2 lie along x-axis and y-axis respectively. Let S be the circle x2+(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=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 ellipse whose centres are at the origin. The major axes of $E_{1}$ and $E_{2}$ lie along x-axis and y-axis respectively. Let S be the circle $x^{2} + (y - 1)^{2} = 2$ the straight line $x + y = 3$ touches the curves S, $E_{1}$ and $E_{2}$ at P, q and R, respectively. Suppose that $P Q = P R = \frac{2 \sqrt{2}}{3} .$ If $e_{1}$ and $e_{2}$ are the eccentricities of $E_{1}$ and $E_{2}$ respectively, then the correct expression(s) is/are