Question

The joint equation of the pair of lines through (3, 2) and parallel to the lines $x=2$ & $y=3$ is:

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

Answer 1

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

The joint equation of pair of lines through $(3,2)$parellel to the lines $x=2$ and $y=3$ is

$(x-2)(y-3)+\lambda =0$

$⟹xy-2y-3x+6+\lambda =0$

Since it passes through $(3,2)$

$\therefore 3\times 2-2\times 3-3\times 2+6+\lambda =0⟹\lambda =0$

So, the equation is $xy-2y-3x+6=0$