Area of the triangle formed by the line and angle bisectors of the pair of straight lines is [2004]

Question

Area of the triangle formed by the line $x + y = 3$ and angle bisectors of the pair of straight lines $x^{2} - y^{2} + 2 y = 1$ is [2004]

Smart Achievers · Accepted Answer

(1)

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

$∴$ $Area between x = 0, y = 1 and x + y = 3 is the shaded region shown in figure.$

$∴$ $Area = \frac{1}{2} \times 2 \times 2 = 2 sq. units$

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