JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)
Let C be the circle x2 + (y-1)2 = 2, E_1 and E_2 be two ellipses whose centres lie at the origin and major axes lie on the x-axis and y-axis respectively. Let the straight line x + y = 3 touch the curves C, E_1 and E_2 at P(x_1,y_1), Q(x_2,y_2) and R(x_3,y_3) respectively. Given that P is the midpoint of the line segment QR and PQ = \frac{2\sqrt{2}}{3}, the value of 9(x_1y_1 + x_2y_2 + x_3y_3) is equal to _____