The area (in sq unit) of the triangle formed by `x+y+1=0` and the pair of straight lines `x^2-3xy+2y^2=0` is

Options

A. `(7)/(12)`
B. `(5)/(12)`
C. `(1)/(12)`
D. `(1)/(6)`

Answer

C

Explanation

Given, `x^(2)-2xy-xy+2y^(2)=0`
`implies(x-2y)(x-y)=0`
`impliesx=2y" "......(i)`
`x=y" "......(ii)`
Also, `x+y+1=0" "......(iii)`
On solving Eqs. (i) and (ii) and (iii), we get
`A(-(2)/(2),(1)/(3)),B(-(1)/(2),(1)/(2)),C(0,0)`
`:."Area of "DeltaABC=(1)/(2)|{:(-(2)/(3),-(1)/(3),1),(-(1)/(2),-(1)/(2),1),(0,0,1):}|`
`=(1)/(2)[(1)/(3)-(1)/(6)]`
`=(1)/(2)[(1)/(6)]=(1)/(12)`