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x^2 + y^2 = 4 is a circle with center (0,0) and radius 2. Plot it on a paper. y=x is a line passing through (0,0) at 45degrees in the second quadrant. y=-x is a line passing through (0,0) at 45 degrees in the first quadrant.
so the angle between two lines is 2(pi/4) = pi/2 = 90 degrees area of sector = (pi * r^2 ) / 4 = pi ans. C