Question

The area of the triangle formed by the lines x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y = 1 is

(A) 2 sq. unit

(B) 4 sq. unit

(C) 6 sq. unit

(D) 8 sq. unit

Answer 1

Correct option**(A) 2 sq. unit**

Explanation :

The given lines are

x2 - (y - 1)2 =0

(x + y - 1) = 0

Therefore, the given lines are x - y + 1 = 0 and x + y - 1 = 0 whose angular bisectors are

That is, y - 1 = 0 and x = 0. Thus, the vertices of the triangle are (0, 1), (0, 3) and (2, 1). Hence, the area is

1/2[0(3 - 1) + 0(1 - 1) + 2(1 - 3)] = 2 sq. unit