Question

Determine the equation of the line that has a distance 2 from the origin and is
parallel to the line that passes thru P1(2,7) and P2(-3,-2).

Answer 1

Distance of line from origin d=2

Since the required line is parallel to the line formed by joining $P_1(2,7) and P_2(-3,-2)$ ,

There slope must be equal

Let m be the slope of required line

$m=\frac{-2-7}{-3-2}$

$=\frac{-9}{-5}$

so m=$\frac{9}{5}$

Let the equation of required line be

$y=mx+c$

$y=\frac{9}{5}x+c$

Rearranging the equation as,

$9x-5y+5c=0$

Distance from origin is given by,

d=$\frac{|9\times 0+0\times -5+5c|}{\sqrt{9^2+(-5)^2}}$

2=$\frac{5c}{\sqrt{106}}$

5c=$2\sqrt{106}$

c=0.4$\sqrt{106}$

So the equation of required line is

9x-5y+2$\sqrt{106}$ =0