First slide

Equation of line in Straight lines

Question

If the distance between the parallel lines $3 x + 4 y + 7 = 0$ and $a x + y + b = 0$ is $1$ , the integral value of $b$ is

Moderate

A

1
B

2
C

3
D

4

Solution

Since the given lines are parallel. Slopes of the lines are equal so $a = \frac{3}{4}$ and the two lines are $3 x + 4 y + 7 =$ and $3 x + 4 y + 4 b = 0$ .
Distance between them is $\frac{| 7 - 4 b |}{\sqrt{3^{2} + 4^{2}}} = 1$
$\Rightarrow 7 - 4 b = \pm 5 \Rightarrow b = 1 / 2$ or $3$

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