AP EAMCET2004MathematicsPair of Lines
Area of the triangle formed by the lines 3 x^2-4 x y+y^2=0,2 x-y=6 is
Options
- A16 sq units
- B25 sq units
- C36 sq units
- D49 sq units
Correct answer
C. 36 sq units
Step-by-step solution
Given lines are aligned & 3 x^2-4 x y+y^2=0 & 3 x^2-3 x y-x y+y^2=0 &(3 x-y)(x-y)=0 & 3 x-y=0, x-y=0 & and 2 x-y=6 aligned The point of intersection of these lines are (0,0),(-6,-18) and (6,6) . aligned Area of triangle & = 1 2 | array lll x₁ & y₁ & 1 x₂ & y₂ & 1 x₃ & y₃ & 1 array | & = 1 2 | array ccc 0 & 0 & 1 -6 & -18 & 1 6 & 6 & 1 array | & = 1 2 (36+108)= 1 2 & =36 sq unit aligned