The equation of the pair of lines through the point $(2,1)$ and perpendicular to the pair of lines $4 x y+2…
The equation of the pair of lines through the point $(2,1)$ and perpendicular to the pair of lines $4 x y+2 x+6 y+3=0$ is
$x y-x-2 y+2=0$
$x y+x-2 y-2=0$
$x y+x+2 y-6=0$
$x y-x+2 y-2=0$
Solution
Given pair of lines,
$
\begin{aligned}
& 4 x y+2 x+6 y+3=0 \\
\Rightarrow \quad & 2 x(2 y+1)+3(2 y+1)=0 \\
\Rightarrow \quad & (2 x+3)(2 y+1)=0
\end{aligned}
$
So, equations of lines are $x=\frac{-3}{2}$ and $y=-\frac{1}{2}$
Equations of line passing through $(2,1)$ and perpendicular to the pair of lines $4 x y+2 x+6 y+3=0$ are
$
y-1=0 \text { and } x-2=0
$
$\therefore \quad$ Combining the equation of lines are
$
(y-1)(x-2)=0 \Rightarrow x y-x-2 y+2=0
$