Straight Line and Pair of Straight Lines 4 Question 2
2. Area of triangle formed by the lines $x+y=3$ and angle bisectors of the pair of straight lines $x^{2}-y^{2}+2 y=1$ is
(a) 2 sq units
(b) 4 sq units
(c) 6 sq units
(d) 8 sq units
(2004, 2M)
Analytical & Descriptive Question
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Answer:
Correct Answer: 2. (a)
Solution:
- Given, $x^{2}-y^{2}+2 y=1$
$$ \begin{aligned} \Rightarrow & x^{2} & =(y-1)^{2} \\ \Rightarrow & x & =y-1 \text { and } x=-y+1 \end{aligned} $$
Angle bisector
From the graph, it is clear that equation of angle bisectors are
$$ \begin{array}{ll} & y=1 \\ \text { and } & x=0 \end{array} $$
$\therefore$ Area of region bounded by $x+y=3, x=0$ and $y=1$ is $\Delta=\frac{1}{2} \times 2 \times 2=2$ sq units
