If the curve x2+2y2=2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ is at the origin is

Equation of the curve is x2+2y2=2⇒x22+y21=1            Equation of the line is  x  + y = 1   ; y = 1-x            Solving the above two equations x2+21-x2=2x2+2x2+2−4x=23x2−4x=0x3x−4=0Hence the values of x are 0,43Hence, the points are  P(0,1)  ,Q43,−13The line OP is vertical axis, the slope of OQ is -14hence the angle subtended by OP and OQ at origin is   θ=  π2+tan-1(-14)   θ = π2+tan-114