Area of the triangle formed by the line x+y=3 and angle bisectors...

Area of the triangle formed by the line

x+y=3

and angle bisectors of the pair of straight lines

x²-y²+2 y=1

Options

A2 sq. units
B4 sq. units
C6 sq. units
D8 sq. units

Correct answer

A. 2 sq. units

Step-by-step solution

(

\mathrm{x}^

\mathrm{y}^

2+2

\mathrm{y}=

1 \Rightarrow

\mathrm{x}= \pm(\mathrm{y}-

1)) Bisectors of above line are (x=0 ~\&~ y=1) Area of the triangle formed by the line x+y=3 and angle bisectors of the pair of straight lines x²-y²+2 y=1 is

So area between (x=0, y=1 ~\&~ x+y=3) is shaded Region shown in figure. Area of the triangle formed by the line x+y=3 and angle bisectors of the pair of straight lines x²-y²+2 y=1 is

Area (=1 / 2

\times

\times

2=2) sq. units

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