Manipal MET2020MathematicsStraight Lines
The three lines of a triangle are given by (x^2-y^2 )(2 x+3 y-6)=0 . If the point (-2, ) lies inside and ( , 1) lies outside the triangle, then
Options
- A(1, 10 3 ) ; (-3,5)
- B(2, 10 3 ) ; (-1,1)
- C(-1, 9 2 ) ; (-2, 10 3 )
- DNone of the above
Correct answer
D. None of the above
Step-by-step solution
Three lines of triangle are given by (x^2-y^2 )(2 x+3 y-6)=0 (x-y)(x+y)(2 x+3 y-6)=0 The three lines of triangle are x-y=0, x+y=0 and 2 x+3 y-6=0 From given lines of triangle, the required O A B is formed. (-2, ) lies inside the triangle. 2(-2)+3( )-6 0 and -2+ 0 array lr & -4+3 -6 0 and 2 & 3 10 and 2 & 10 3 and 2 array 0 (2+8 (2 10 3 ) . ....(i) Now, ( , 1) lies outside the triangle. To find value of , we find the interval [M, N for values of x . x+1 0 and x-1 0 array lr & x -1 and x 1 & x [-1,1] array ( , 1) lie