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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)))|`

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

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

Knowledge Check

  • 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`

  • 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

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

    A
    `|d-d^(')|/(sqrt""(a^(2)+b^(2)+c^(2)))`
    B
    `|d+d^(')|/(sqrt""(a^(2)+b^(2)+c^(2)))`
    C
    `d/(sqrt""(a^(2)+b^(2)+c^(2)))`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    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

    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)))

    Assertion: The distance between two parallel planes ax+by+cz+d=0 and ax+by+cz+d\'=0 is (|d-d\'|)/sqrt(a^2+b^2+c^2) , Reason: The normal of two parallel planes are perpendicular to each other. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

    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 ?

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