Question

Find the joint equation of the lines which pass through the point (4, -3) and are parallel to the lines x = 1 and y = 5.

Answer 1

The line parallel to the line $x=1$ will be of the form $x=c$

Now, $x=c$ passes through the point $(4,-3)$

So,

$4=c$

And the line is $x=4$

$x-4=0$ ........... (1)

The line parallel to the line $y=5$ will be of the form $y=k$

Now, $y=k$ passes through the point $(4,-3)$

So,

$-3=k$

And the line is $y=-3$

$y+3=0$ ........... (2)

Joint equation of the lines is,

$(x-4)(y+3)=0$

$3x-4y+xy-12=0$