Ncert Solutions Maths class 11th

Let C be the circle x² + (y - 1)² = 2, E? and E? 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, E?, and E? at P(x?, y?), Q(x?, y?), and R(x?, y?) respectively. Given that P is the mid-point of the line segment QR and PQ = 2√2/3, the value of 9(x?y? + x?y? + x?y?) is equal to ___.