Question

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

• A. 2 sq. units
• B. 4 sq. units
• C. 6sq. units
• D. 8 sq. units

Answer 1

The correct option is A 2 sq. units

$x^2-y^2+2y=1\Rightarrow x=\pm (y-1)$




Bisectors of above lines are $x=0$ and $y=1$.

So area between $x=0,y=1$ and $x+y=3$ is shaded region shown in figure.
$\text{Area}=\frac{1}{2}\times 2\times 2=2$ sq.units.