Question

Find the equations of the lines through the point of intersection of the lines $x+2y-6=0$ and $7x-y-12=0$ each of which is at a distance of $2$ units from the origin.

• A. $x=2$ and $y=2$
• B. $x=0$ and $y=2$
• C. $x=2$ and $y=0$
• D. $x=-2$ and $y=2$

Answer 1

The correct option is A $x=2$ and $y=2$

$x+2y-6=0$ .................... (1)

$7x-y-12=0$ ................... (2)

Multiply (2) with $2$ ,

$14x-2y-24=0$ .................. (3)

Adding (1) and (3) ,

$15x-30=0$

$x=2$

From (1),

$2y=6-x$

$2y=4$

$y=2$

So, point of intersection is $(2,2)$

Now, we want to find the lines which passes through $(2,2)$ and the perpendicular distance of the line from the origin is $2$ units.

So, one line is $x=2$ ( as $x$-axis is the perpendicular to the line $x=2$ , distance of the line from origin is $2$ units )

And the other line is $y=2$ ( as $y$-axis is the perpendicular to the line $y=2$ , distance of the line from origin is $2$ units )