Find equation of the line parallel to the line 3x − 4y + 2 = 0 and passing through the point (–2, 3). - Noon Academy

Find equation of the line parallel to the line 3x − 4y + 2 = 0 and passing through the point (–2, 3).

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

Find equation of the line parallel to the line 3x − 4y + 2 = 0 and passing through the point (–2, 3).

Given:

The line is

$\mathbf{3x}\text{ }\text{ }\mathbf{-4y}\text{ }+\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{0}$

In this way,

$\mathbf{y}\text{ }=\text{ }\mathbf{3x}/\mathbf{4}\text{ }+\text{ }\mathbf{2}/\mathbf{4}$

$=\text{ }\mathbf{3x}/\mathbf{4}\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}$

Which is of the structure

$\mathbf{y}\text{ }=\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{c}$

, where m is the slant of the given line.

The incline of the given line is

$\mathbf{3}/\mathbf{4}$

We realize that equal line have same slant.

∴ Slope of other line

$=\text{ }\mathbf{m}\text{ }=\text{ }\mathbf{3}/\mathbf{4}$

Condition of line having slant m and going through (x1, y1) is given by

$\mathbf{y}\text{ }\text{ }\mathbf{-y1}\text{ }=\text{ }\mathbf{m}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{x1} \right)$

∴ Equation of line having slant 3/4 and going through (- 2, 3) is

$\mathbf{y}\text{ }\text{ }\mathbf{-3}\text{ }=\text{ }{\scriptscriptstyle 3\!/\!{ }_4}\text{ }\left( \mathbf{x-}\text{ }\text{ }\left( -\text{ }\mathbf{2} \right) \right)$

$\mathbf{4y-}\text{ }\text{ }\mathbf{3}\text{ }\times \text{ }\mathbf{4}\text{ }=\text{ }\mathbf{3x}\text{ }+\text{ }\mathbf{3}\text{ }\times \text{ }\mathbf{2}$

$\mathbf{3x-}\text{ }\text{ }\mathbf{4y}\text{ }=\text{ }\mathbf{18}$

∴ The condition is

$\mathbf{3x-}\text{ }\text{ }\mathbf{4y}\text{ }=\text{ }\mathbf{18}$

i

More Material

Find the angle between each of the following pairs of lines:

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A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

A line passes through the point (3, 4, 5) and is parallel to the vector Find the equations of the line in the vector as well as Cartesian forms.

Evaluate:

Evaluate:

Evaluate:

If $f(x) = |x| - 3,find\mathop {\lim }\limits_{x \to 3} f(x)$

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{x}{{|x|}},x \ne 0\\ 0,x = 0 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} f(x) \end{array}$ does not exist.

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{|x-3|}{{(x-3)'}},x \ne 3\\ 0,x = 3 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 3} f(x) \end{array}$ does not exist.

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