The area (in sq. units) of the triangle formed by the straight line x + y = 3 and the angular bisectors of the pair of straight lines x 2 - y 2 + 2 y = 1 is

Step-by-step solution

Pair of straight line is x 2 - y 2 + 2 y = 1 ⇒ x 2 - y 2 + 2 y - 1 = 0 ⇒ x 2 - y - 1 2 = 0 ⇒ x - y + 1 x + y - 1 = 0 Therefore, we get the separate equations of two straight lines l 1 : x - y + 1 = 0     . . . i l 2 : x + y - 1 = 0     . . . ii Now, point of intersection of line l 1 and x + y = 3 is A 1 , 2 . Now, required area is ar ∆ A B C = 1 2 × B C × A D . = 1 2 × 2 × 1 = 1   sq. units