The area of the triangle formed by the line x+y=4 and angular bisectors of the pair of lines x^2-y^2+2 y-1=0 is......... sq. units.

Step-by-step solution

Given, pair of lines is x^2-y^2+2 y-1=0x^2=y^2-2 y+1 x^2=(y-1)^2 aligned & (x+y-1)(x-y+1)=0 & x+y-1=0 or x-y+1=0 aligned 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 A F is the angle bisector lines for the given pair of lines. The required triangle is A B F . Area of A B F= 1 2 A F A B ...(i) Lets find point F which is the intersection point of x+y=4 and y=1 x+1=4 x=3 A F=3, A B=3 ar ( A B F)= 1 2 3 3=4.5 sq units