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

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.

Approved