Question

The joint equation of the pair of lines passing through $(2,3)$ and parallel to the coordinates axes is

• A. $xy-3x-2y+6=0$
• B. $xy+3x+2y+6=0$
• C. $xy=0$
• D. $xy-3x-2y-6=0$

Answer 1

The correct option is A $xy-3x-2y+6=0$

Equation of the coordinate axes are $x=0$ and $y=0$.
Therefore, the equations of the lines passing through $(2,3)$ and parallel to coordinate axes are,
$x=2$ and $y=3$.
i.e., $x-2=0$ and $y-3=0$
The joint equation is given as
$(x-2)(y-3)=0$

$\Rightarrow x(y-3)-2(y-3)=0$
$\Rightarrow xy-3x-2y+6=0$
Hence, the correct answer from the given alternative is option A.