First slide

Pair of straight lines

Question

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

Moderate

A

2sq. units
B

4sq. units
C

6sq. units
D

8sq. units

Solution

$x^{2} - y^{2} + 2 y = 1$ or $x = \pm (y - 1)$
The bisectors of the above lines are x=0 and y=1
So, the area between x=0,y=1, and x+y=3 is the shaded region shown in the figure. The area is given by $(1 / 2) \times 2 \times 2 = 2$ sq.units

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