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Find the distance between the parallel lines `3x 4y + 7 = 0`and`3x 4y + 5 = 0`.

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To find the distance between the two parallel lines given by the equations \(3x + 4y + 7 = 0\) and \(3x + 4y + 5 = 0\), we can follow these steps: ### Step 1: Identify the coefficients The equations of the lines can be rewritten in the form \(Ax + By + C = 0\): - For the first line \(3x + 4y + 7 = 0\), we have \(A = 3\), \(B = 4\), and \(C_1 = 7\). - For the second line \(3x + 4y + 5 = 0\), we have \(C_2 = 5\). ### Step 2: Use the distance formula for parallel lines ...
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Knowledge Check

  • Find the distance between the parallel lines 3x+4y-7=0 and 3x+4y+8=0 .

    A
    `1` units.
    B
    `2` units.
    C
    `3` units.
    D
    `4` units.
  • The distance between the parallel lines 3x - 4y + 9 =0 and 6x - 8y - 17 =0 is-

    A
    `(5)/(2)` units
    B
    3 units
    C
    `(7)/(2)` units
    D
    4 units
  • Find the distance between two parallel lines 5x + 12y - 30 = 0 and 5x + 12y - 4 = 0

    A
    3
    B
    7
    C
    44318
    D
    2
  • NCERT-STRAIGHT LINES-SOLVED EXAMPLES
    1. Find the distance between the parallel lines 3x 4y + 7 = 0and3x 4y ...

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    2. Find the distance of the point (3, - 5)from the line 3x - 4y - 26 =0.

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    3. Find the equation of the line whose perpendicular distance from the or...

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    4. Find the equation of the line, which makes intercepts 3 and 2 on the x...

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    5. Equation of a line is 3x-4y+10=0. Find its (i) slope, (ii) x and yin...

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    6. The Fahrenheit temperature F and absolute temperature K satisfy a lin...

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    7. Find the angle between the lines y-sqrt(3)x-5=0and sqrt(3)y-x+6=0.

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    8. Reduce the equation sqrt(3)x+y-8=0 into normal form. Find the values ...

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    9. Find the equation of a line perpendicular to the line x-2y+3=0and pas...

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    10. Show that two lines a1x+b1y+c1=0and a2x+b2y+c2=0, where b1,b2!=0are : ...

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    11. If the lines 2a + y 3 = 0, 5x + k y 3 = 0and 3x y 2 = 0are concurr...

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    12. Find the distance of the line 4x y = 0 from the point P(4, 1) measur...

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    13. Assuming that straight lines work as the plane mirror for a point, fi...

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    14. Show that the area of the triangle formed by the lines y=m1x+c1,y=m2x...

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    15. A line is such that its segment between the lines 5x-y + 4 = 0and 3x ...

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    16. Show that the path of a moving point such that its distances from two...

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    17. Write the equation of the line through the points (1, 1)and (3, 5).

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    18. Write the equation of the line for which tantheta=1/2,where thetais th...

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    19. Find the equations of the lines parallel to axes and passing through(...

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    20. Find the equation of the line through ( 2, 3)with slope 4.

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