AP EAMCET202119 Aug 2021Evening ShiftMathematicsPair of LinesActual
The equation 8 x 2 - 24 x y + 18 y 2 - 6 x + 9 y - 5 = 0 represents a
Options
- Apair of perpendicular lines
- Bpair of parallel lines
- Cpair of coincident lines
- Dparabola
Correct answer
B. pair of parallel lines
Step-by-step solution
We know that a general equation of second degree a x 2 +   2 h x y +   b y 2   +   2 g x   +   2 f y   +   c   =   0     . . . 1 represents a pair of straight line if a h g h b f g f c = 0 and h 2 > 0 , And 1 represents a pair of parallel lines, if f · g ≠ 0 ,   b g 2 = a f 2 = k ≥ a b c   for   a > 0   and   k ≤ a b c   for   a < 0 . We have the equation 8 x 2 - 24 x y + 18 y 2 - 6 x +