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. $6$ sq. units
• D. $8$ sq. units

Answer 1

The correct option is A $2$ sq. units

Equation of angle bisector of $x^2-y^2+2y-1=0$ $\Rightarrow x^2-{y-1}^2=0$ is

$\Rightarrow \frac{x^2-{(y-1)}^2}{1-(-1)}=\frac{x(y-1)}{0}\Rightarrow x(y-1)=0$

$\Rightarrow x=0$ or $y-1=0$

Area of traingle=$\frac{1}{2}\times base\times height$

$\Rightarrow$ Area of triangle $=\frac{1}{2}\times 2\times 2=2$ sq. units