Question

Area of the triangle formed by the line x + y = 3 and the angle bisectors of the pair of lines x2 – y2 + 2y - 1 = 0

(A) 2

(B) 4

(C) 6

(D) 8

Answer 1

Correct option (a) 2

Explanation :

x2 - y2 + 2y - 1 = 0

x2- (y - 1)2 = 0

(x + y -1)(x - y + 1) = 0

Therefore, the pair of lines is x + y -1 = 0 and x - y + 1 = 0 and their angle bisectors are

That is y = 1 and x = 0. Therefore, the sides of the triangle are x = 0, y= 1 and x + y = 3. The vertices are (0, 1), (0, 3) and (2, 1). Hence the area of the triangle is