Prove that distance between two parallel lines `ax+by+c_1=0` and `ax+by+c_2=0` is given by `|c_1-c_2|/(sqrt(a^2+b^2))`.

Distance between the parallel lines ax + by +c_1 = 0 and ax + by + c_2 = 0 is

Distance between the parallel lines ax + by +c_1 = 0 and ax + by + c_2 = 0 is

Distance between the parallel lines ax + by +c_1 = 0 and ax + by + c_2 = 0 is

Find the distance between the parallel lines ax+by+c=0 and ax+by+d=0

Show that the distance between the parallel lines ax+by+c=0 and k(ax+by)+d=0 is |(c-(d)/(k))/(sqrt(a^(2)+b^(2)))|

Consider the following statements : 1. The distance between the lines y=mx+c_(1) and y=mx+c_(2) is (|c_(1)-c_(2)|)/sqrt(1-m^(2)) . 2. The distance between the lines ax+by+c_(1) and ax+by+c_(2)=0 is (|c_(1)-c_(2)|)/sqrt(a^(2)+b^(2)) . 3. The distance between the lines x=c and x=c_(2) is |c_(1)-c_(2)| . Which of the above statements are correct ?

For a gt b gt c gt 0 if the distance between (1,1) and the point of intersection of the lines ax + by +c=0 and bx + ay+c=0 is less than 2sqrt2 then

For a>b>c>0, if the distance between (1,1) and the point of intersection of the line ax+by-c=0 and bx+ay+c=0 is less than 2sqrt(2) then,(A)a+b-c>0(B)a-b+c 0(D)a+b-c<0