Given, pair of lines is x2−y2+2y−1=0 x2=y2−2y+1 ⇒x2=(y−1)2 ⇒(x+y−1)(x−y+1)=0 ⇒x+y−1=0 or x−y+1=0
l1:x+y−1=0...(i) l2:x−y+1=0 ...(ii) From the diagram, we can see that Y-axis and line passing through AF is the angle bisector lines for the given pair of lines. The required triangle is ΔABF. ∴ Area of ΔABF=
1
2
×AF×AB ...(i) Lets find point F which is the intersection point of x+y=4 and y=1 ∴x+1=4 ⇒x=3 ⇒AF=3,AB=3 ∴ar(ΔABF)=