Area of the triangle formed by the line x+y=3 and the  angle bisectors of the pairs of straight lines x2−y2+2y=1 is

x2−y2+2y=1 or x=±(y−1)The bisectors of the above lines are x = 0 and y = 1. So, the area between x=0,y=1 , and x+y=3 is the  shaded region shown in the figure. The area is given by 12×2×2=2 sq. units.