Answer to Question #135371 in Analytic Geometry for Stinky Socks

Question #135371
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).
1
Expert's answer
2020-09-29T18:01:26-0400

Distance of line from origin d=2

Since the required line is parallel to the line formed by joining P1(2,7)andP2(3,2)P_1(2,7) and P_2(-3,-2) ,

There slope must be equal

Let m be the slope of required line

m=2732m=\frac{-2-7}{-3-2}

=95=\frac{-9}{-5}

so m=95\frac{9}{5}

Let the equation of required line be

y=mx+cy=mx+c

y=95x+cy=\frac{9}{5}x+c

Rearranging the equation as,

9x5y+5c=09x-5y+5c=0


Distance from origin is given by,

d=9×0+0×5+5c92+(5)2\frac{|9\times 0+0\times -5+5c|}{\sqrt{9^2+(-5)^2}}


2=5c106\frac{5c}{\sqrt{106}}


5c=21062\sqrt{106}


c=0.4106\sqrt{106}

So the equation of required line is


9x-5y+2106\sqrt{106} =0

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