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Question
The distance between the lines y = mx + c1 and y = mx + c2 is ______.
Options
`(c_1 - c_2)/sqrt(m^2 + 1)`
`|c_1 - c_2|/sqrt(1 + m^2)`
`(c_2 - c_1)/sqrt(1 + m^2)`
0
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Solution
The distance between the lines y = mx + c1 and y = mx + c2 is `|c_1 - c_2|/sqrt(1 + m^2)`.
Explanation:
Given equations are y = mx + c1 .....(i)
And y = mx + c2 .....(ii)
Slopes of equation (i) and equation (ii) are same
i.e., m
So, they are parallel lines.
∴ Distance between the two lines = `|c_1 - c_2|/sqrt(1 + m^2)`.
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