Question

Area of triangle formed by the lines $x + y = 3$ 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

Answer: (A)

2 sq units

Answer 2

Given, $x^2 - y^2 + 2y = 1$
$\Rightarrow x^2 = ( y - 1)^2$
$\Rightarrow x = y - 1$
and x = - y + 1

From the graph, it is clear that equation of angle bisectors are $y = 1$ and $x = 0$
$\therefore$ Area of region bounded b y x + y = 3 ,x = 0 and y = 1 is
$\triangle = \frac{1}{2} \times 2 \times 2 = 2$ sq units.