Question

The equation $6x^2+xy-12y^2-13x+6y+6=0$ represents

• A. a pair of straight lines through the origin
• B. a pair of perpendicular straight lines
• C. a pair of parallel straight lines
• D. a pair of straight lines not passing through the origin, neither parallel nor perpendicular

Answer 1

Answer: (D)

We have,
$6x^2+xy-12y^2-13x+6y+6=0$
Here, $a=6,h=\frac{1}{2},b=-12$,
$g=-\frac{13}{2}$
$f=3,c=6$
$\because a+b=6-12=-6\ne 0$
$\therefore$ A pair of line is not perpendicular and
$\because h^2\ne ab$
$\therefore$ Pair of line is not parallel
Hence, pair of straight line is not passing through origin, neither parallel nor perpendicular.