Area of the triangle formed by the line \(x+y=3\) and angle bisectors of the pair of straight lines \(x^2-y^2+2 y=1\) is

• Correct answer
  A

  2 sq. units
• B

  4 sq. units
• C

  6 sq. units
• D

  8 sq. units

Solution

\(\mathrm{x}^2-\mathrm{y}^2+2 \mathrm{y}=1 \Rightarrow \mathrm{x}= \pm(\mathrm{y}-1)\) Bisectors of above line are \(x=0 ~\&~ y=1\)
So area between \(x=0, y=1 ~\&~ x+y=3\) is shaded Region shown in figure.
Area \(=1 / 2 \times 2 \times 2=2\) sq. units

Hence, the correct answer is option: 'A'.