Equation of line in Straight lines

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Question

If the distance between parallel lines 3x + 4y +7 = 0 and ax + y + b = 0 is 1 , then sum of values of b is

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Solution

Since lines are parallel, we have $- \frac{3}{4} = - \frac{a}{1}$
$\Rightarrow a = \frac{3}{4}$
So, lines are 3x + 4y + 7 = 0 and 3x + 4y + 4b =0 Distance between lines = 1
$\begin{aligned} \Rightarrow \frac{| 7 - 4 b |}{\sqrt{3^{2} + 4^{2}}} = 1 \Rightarrow 7 - 4 b = 5 o r 7 - 4 b = - 5 \\ \Rightarrow b = \frac{1}{2}, 3 \end{aligned}$

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

If the distance between parallel lines 3x + 4y +7 = 0 and ax + y + b = 0 is 1 , then sum of values of b is

Since lines are parallel, we have −34=−a1⇒a=34So, lines are 3x + 4y + 7 = 0 and 3x + 4y + 4b =0 Distance between lines = 1⇒|7−4b|32+42=1⇒7-4b=5 or 7-4b=-5 ⇒ b=12,3

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