Find the distance between parallel lines (i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l(x + y) + p = 0 and l (x + y)

Find the distance between parallel lines (i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l(x + y) + p = 0 and l (x + y) – r = 0

Class 11 | Exercise 10.3 | Maths | NCERT | Straight Lines

Find the distance between parallel lines (i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 (ii) l(x + y) + p = 0 and l (x + y) – r = 0

$\left( \mathbf{i} \right)\text{ }\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }\text{ }\mathbf{34}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }+\text{ }\mathbf{31}\text{ }=\text{ }\mathbf{0}$

Given:

The equal lines are

$\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }\text{ }\mathbf{34}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }+\text{ }\mathbf{31}\text{ }=\text{ }\mathbf{0}.$

By utilizing the equation,

The distance (d) between equal lines

$\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C1}\text{ }=\text{ }\mathbf{0}$

and

$\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C2}\text{ }=\text{ }\mathbf{0}$

is given by

∴ The distance between equal lines is

$\mathbf{65}/\mathbf{17}$

$\left( \mathbf{ii} \right)\text{ }\mathbf{l}\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }+\text{ }\mathbf{p}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{l}\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }\text{ }\mathbf{r}\text{ }=\text{ }\mathbf{0}$

Given:

The equal lines are

$\mathbf{l}\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }+\text{ }\mathbf{p}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{l}\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }\text{ }\mathbf{r}\text{ }=\text{ }\mathbf{0}.$

$\mathbf{lx}\text{ }+\text{ }\mathbf{ly}\text{ }+\text{ }\mathbf{p}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{lx}\text{ }+\text{ }\mathbf{ly}\text{ }\text{ }\mathbf{r}\text{ }=\text{ }\mathbf{0}$

by utilizing the equation,

The distance (d) between equal lines

$\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C1}\text{ }=\text{ }\mathbf{0}$

and

$\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C2}\text{ }=\text{ }\mathbf{0}$

is given by