Question

distance between the two parallel lines 2x-y+7=0 & 2x-y+5=0 is​

Answer 1

Answer:

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Answer 2

Answer: The distance between two parallel lines is $\frac{2}{\sqrt{5} }$.

Step-by-step explanation:

Given: Two parallel lines $2x-y+7=0$

                                 and    $2x-y+5=0$

To find: We have to find the distance between the two parallel lines.

Solution:

Step 1: The formula of distance between parallel lines is given by,

                                   $D = \frac{C_{1}-C_{2} }{\sqrt{a^{2}+b^{2} } }$

         where , $C_{1} =7,C_{2} =5,a=2,b=-1$

∴                                  $D =\frac{7-5}{\sqrt{2^{2}+(-1)^{2} } }$

                                   $D=\frac{2}{\sqrt{4+1} }$

  Hence, the distance between two parallel lines is $\frac{2}{\sqrt{5} }$

Concept: The distance between two parallel lines is equal to the perpendicular distance between the two lines. We know that the slopes of two parallel lines are the same; therefore, the equation of two parallel lines can be given as: y = mx + c1…. (1) and y = mx + c2…. (2)

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