First slide

Equation of line in Straight lines

Question

The distance between the parallel lines $y = 2 x + 4$ and $6 x = 3 y + 5,$ is

Moderate

A

$\frac{17}{\sqrt{3}}$
B

$1$
C

$\frac{3}{\sqrt{5}}$
D

$\frac{17 \sqrt{5}}{15}$

Solution

$2 x - y + 4 = 0$ and $6 x - β y - 5 = 0$
$\Rightarrow 2 x - y + 4 = 0$ and $2 x - y - \frac{5}{3} = 0$
The distance between these two parallel lines is given by
$d = |\frac{4 + \frac{5}{3}}{\sqrt{2^{2} + (- 1)^{2}}}| = \frac{17 \sqrt{5}}{15}$

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