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a)) show that the distance d between the parallel lines Ax+By+C1=0 and Ax+By+C2=0 in the plane is : d=l C1 - C2 l/ A^2 + B^2 b)) use this result to find the distance between the parallel lines 2x+3y+17=0 and 4x+6y+31=0

a)) show that the distance d between the parallel lines Ax+By+C1=0 and Ax+By+C2=0 in the plane is :


d=l C1 - C2 l/\sqrt{\ } \!\,A^2 + B^2


 


b)) use this result to find the distance between the parallel lines 2x+3y+17=0  and 4x+6y+31=0


 

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1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

The two lines have the same slope equal to -A/B. The equation of the common normal from the origin to the two lines is

y=Bx/A, find the point of intersection of this normal with each of the two lines. The distance between the two lines is the same as the distance between these two points.

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