Area of triangle formed by the lines and angle bisectors of the pair of straight lines is
- A.2 sq units
- B.4 sq units
- C.6 sq units
- D.8 sq units
Show answer and solution
Correct option: A
Solution
The pair x² - y² + 2y = 1 rewrites as x² - (y-1)² = 0, giving lines x = y-1 and x = -(y-1), i.e., x - y + 1 = 0 and x + y - 1 = 0.
These two lines intersect at (0,1). Their angle bisectors are the horizontal and vertical lines through (0,1): y = 1 (bisector of the acute angle) and x = 0 (bisector of the obtuse angle).
The three lines forming the triangle are x = 0, y = 1, and x + y = 3. Their vertices are: (0,1)∩x=0 gives (0,1); x=0 and x+y=3 gives (0,3); y=1 and x+y=3 gives (2,1).
Area = (1/2) × base × height = (1/2) × 2 × 2 = 2 sq units.
These two lines intersect at (0,1). Their angle bisectors are the horizontal and vertical lines through (0,1): y = 1 (bisector of the acute angle) and x = 0 (bisector of the obtuse angle).
The three lines forming the triangle are x = 0, y = 1, and x + y = 3. Their vertices are: (0,1)∩x=0 gives (0,1); x=0 and x+y=3 gives (0,3); y=1 and x+y=3 gives (2,1).
Area = (1/2) × base × height = (1/2) × 2 × 2 = 2 sq units.
[AIEEE 2004]