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

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

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)))

Knowledge Check

  • Consider the following statements : I . The distance between the lines y = mx + c_(1) and y = mx + c_(2) is (|c_(1) - c_(2)|)/(sqrt(1 -m^(2))) II . The distance between the lines ax + by + c_(1) = 0 and ax + by + c_(2) = 0 is (|c_(1) - c_2|)/(sqrt(a^(2) + b^(2))) III . The distance between the lines x = c and x = c_(2) is |c_(1) - c_(2)| Which of the above statements are correct ?

    A
    I and II only
    B
    II and III only
    C
    I and III only
    D
    I , II and III only

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

    A
    `| (d-c)/( sqrt(a^2 + b^2 ) )|`
    B
    `| (d-c)/( sqrt(a^2 - b^2 ) )|`
    C
    `(d-c)/( sqrt(ab)`
    D
    `d-c`

  • If the distance between the parallel lines 3x+4y+7=0 and ax+y+b=0 is 1, the intergral value of b is

    A
    1
    B
    2
    C
    3
    D
    4

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    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)))|

    If aa^1= b b^1 != 0, the points where the coordinate axes cut the lines ax + by + c=0 and a^1 x + b^1 y+c^1=0 form

    The distance the parallel planes ax+by+cz+d=0 and ax+by+cz+d'=0

    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 ?

    The area of the figure formed by the lines ax + by +c = 0, ax - by + c = 0, ax+ by-c = 0 and ax- by - c = 0 is

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