Question

the distance between the parallel lines 4y-2x+1=0 , x-2y+1=0 is

Answer 1

Answer:

Distance between parallel lines

a1x+b1y+c1=0 and a1x+b1y+c2=0 is |c2-c1|

Answer 2

The distance between given lines is 1/2√5

Given:

4y - 2x + 1 = 0_ Line(1)

x - 2y + 1 = 0 _ Line(2) are 2 parallel lines  

Here Line (1) can be written as

-2y + x + 1/2 = 0 _ Line (1)   [ divided by -2 on both sides ]

To find:

The distance between given 2 parallel lines

Solution:

The formula for the distance between 2 parallel lines ax + by + c = 0 and ax + by + c₁ = 0 is given by d = |c – c₁| /√(a² + b²)

⇒ Here we have lines  x -2y + 1/2 = 0 and x - 2y + 1 = 0  compare these both lines with ax + by + c = 0 and ax + by + c₁ = 0

⇒  a = 1, b = -2 and c = 1 and c₁ = 1/2  

⇒ distance d = |1 – 1/2| /√(1² + (-2)²)  

                      = |1/2| /√(1 + 4)  = (1/2) /√5   = 1/2√5 units

Therefore, the distance between given lines is 1/2√5

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