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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/$\sqrt{\ } \!\,$A^2 + B^2b)) use this result to find the distance between the parallel lines 2x+3y+17=0  and 4x+6y+31=0

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.