BITSAT2016MathematicsPair of LinesActual
The equation x²-2 3 x y+3 y²-3 x+3 3 y-4=0 represents
Options
- Aa pair of intersecting lines
- Ba pair of parallel lines with distance between them 5 2
- Ca pair of parallel lines with distance between them 5 2
- Da conic section, which is not a pair of straight lines
Correct answer
B. a pair of parallel lines with distance between them 5 2
Step-by-step solution
We have a=1, h=- 3 , b=3, g=- 3 2 , f = 3 3 2 , c =-4 Thus a b c+2 f g h-a f²-b g²-c h²=0 Hence the equation represents a pair of straight lines. Again a h = h b = g f =- 1 3 the lines are parallel. The distance between them =2 g²-a c a(a+b) =2 9 4 +4 1(1+3) = 5 2