Question: Find the value of k so that $5x +ky=20$ makes an angle of 60° with x-axis.

Solution:
Given,

Equation of line is $5x + ky = 20$

Slope of the line ($m_1$) = $- \dfrac{coefficient\;of\;x}{coefficient\;of\;y}$
$= - \dfrac{5}{k}$

Angle made by the line with x-axis ($\theta$) = 60° or (180°-60° = 120°)

Slope ($m_2$) =$ tan \theta$
$= tan 60°$
$= \sqrt{3}$

Slope ($m_2$) = $tan \theta$
$= tan 120°$
$= tan (180°-60°)$
$= - tan 60°$
$ = - \sqrt{3}$

We know,
$(m_1\; and\; m_2) \;and\; (m_1 \;and \;m_3)$ represent the slope of the same equation. So,

$m_1 = m_2$
$or, - \dfrac{5}{k} = √3$

$\therefore k = - \dfrac{5}{√3}$

Also,

$m1 = m_3$
$or, - \dfrac{5}{k} = - √3$

$or, \dfrac{5}{k} = √3$

$\therefore k = \dfrac{5}{√3}$

Hence, the possible values of k are $\pm \dfrac{5}{\sqrt{3}}$


Related Notes and Solutions:

Here is the website link to all the important formulae of Coordinate Geometry of Class 10.

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