AP EAPCET 23-Aug-2021 Shift 2 Paper

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)=

1

2

×3×3=4.5 sq units