Circles Part 2

Let C be the circle x2+(y−1)2=2,E1 and E2 be two ellipses whose centres lie at the origin and major axes lie on x-axis and y-axis respectively. Let the straight-line x+y=3 touch the curves C,E1 and E2 at P(x1,y1),Q(x2,y2) and R(x3,y3) respectively. Given that P is the midpoint of the line segment QR and PQ=‌

2√2

3

, the value of 9(x1y1+x2y2+x3y3) is equal to ____