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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