Question

The equation of the pair of lines through the point $(2,1)$ and perpendicular to the pair of lines $4xy+2x+6y+3=0$ is

• A. xy - x - 2y + 2 = 0
• B. xy + x - 2y - 2 = 0
• C. xy + x + 2y - 6 = 0
• D. xy - x + 2y - 2 = 0

Answer 1

Answer: (A)

We have
$4xy+2x+6y+3=0$
$\Rightarrow 2x(2y+1)+3(2y+1)=0$
$\Rightarrow (2x+3)(2y+1)=0$
Equation of lines are $x=\frac{-3}{2}$ and $y=-\frac{1}{2}$
Equations of line passing through $(2,1)$ and
perpendicular to the line $x=\frac{23}{2}$ and $y=\frac{1}{2}$ are
$y-1=0\text{ and }x-2=0$
$\therefore$ Combining equation of lines are
$(y-1)(x-2)=0$
$\Rightarrow xy-x-2y+2=0$