Area of the triangle formed by the line `x+y=3` and angle bisectors of the pair of straight lines `x^2-y^2+2y=1` is `2s qdotu n i t s` b. `4s qdotu n i t s` c. `6s qdotu n i t s` d. `8s qdotu n i t s`

Options

A. 2 sq. units
B. 4 sq. units
C. 6 sq. units
D. 8 sq. units

Answer

A

Explanation

We have,
`x^(2)-y^(2)+2y-1=0" …(i)"`
`rArr" "x^(2)-(y-1)^(2)=0 rArr (x-y+1)(x+y-1)=0`
Thus, the lines given by equation (i) are
`x-y+1=0 and x+y-1=0`
Clearly, these two equations represent a pair of perpendicular lines intersecting at (0, 1). The eqautions of the angle bisectors are `y=1` abd `x=0`.

The line `x+y=3` forms the triangle ABC with the two angle bisectors.
`"Area of "DeltaABC=(1)/(2)(ABxxAC)`
`rArr" Area of "DeltaABC=((1)/(2)xx2xx2)sq. units=2sq. units`