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Home  >>  CBSE XI  >>  Math  >>  Straight Lines
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Choose the correct answer from the given four options. The ratio in which the line $3x + 4y + 2 = 0$ divides the distance between the lines $3x + 4y + 5 = 0$ and $3x + 4y – 5 = 0$ is

$\begin {array} {1 1} (A)\;1 : 2 & \quad (B)\;3 : 7 \\ (C)\;2 : 3 & \quad (D)\;2 : 5 \end {array}$

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Toolbox:
  • The distance between parallel line is $ d = \bigg| \large\frac{c_1-c_2}{\sqrt{a^2+b^2}} \bigg|$
Step 1 :
The equation of the given lines are
$ 3x+4y+5=0 $ ------(1) and
$ 3x+4y-5=0$-------(2)
Since both the lines have same slopes, the lines are parallel.
Equation of the line which divides the distances between these two lines is $3x+4y+2$--------(3)
This line also has the same slope.
Distance between lines (1) and line (3) is
$ d_1 \bigg| \large\frac{5-2}{\sqrt{3^2+4^2}} \bigg|$$ = \large\frac{3}{5}$
Distance between line (2) and line (3) is
$ d_2 = \bigg| \large\frac{-5-2}{\sqrt{3^2+4^2}} \bigg|$
$ = \large\frac{7}{5}$
Hence $d_1 : d_2 = 3 : 7$
$ \therefore $ 'B' is the correct answer.
answered Jul 6, 2014 by thanvigandhi_1
 

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