Find the equations of two lines each parallel to $3 x + 4 y + 7 = 0$ one of which passes through $(1, 1)$ and other through $(- 2, - 1)$ . Also find the perpendicular distance between them.

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Solution

The required lines are
$3 x + 4 y - 7 = 0$ and $3 x + 4 y + 10 = 0$
$p_{1} = - 7 / 5$ , $p_{2} = 10 / 5$
$∴ d =$ distance between parallel lines,
$= p_{1} - p_{2} = - \frac{7}{5} - \frac{10}{5}$
$= - \frac{17}{5} = \frac{17}{5}$ numerically.

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