(D) The normal form of the equation of a line is given by $x \cos \alpha + y \sin \alpha = p$,where $p$ is the length of the perpendicular from the or

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(D) The normal form of the equation of a line is given by $x \cos \alpha + y \sin \alpha = p$,where $p$ is the length of the perpendicular from the origin to the line and $\alpha$ is the angle that the perpendicular makes with the positive $X$-axis.Given $p = 4$ and $\alpha = 30^{\circ}$.Substituting these values into the formula:$x \cos 30^{\circ} + y \sin 30^{\circ} = 4$$x \left(\frac{\sqrt{3}}{2}\right) + y \left(\frac{1}{2}\right) = 4$Multiplying both sides by $2$,we get:$\sqrt{3} x + y = 8$

Class 11 Mathematics Straight Lines Slope of line, Equation of line in different forms

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The equation of the line,where the length of the perpendicular segment from the origin to the line is $4$ and the inclination of this perpendicular segment with the positive direction of the $X$-axis is $30^{\circ}$,is:

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A
$x+\sqrt{3} y=8$
B
$x-\sqrt{3} y=8$
C
$\sqrt{3} x-y=8$
D
$\sqrt{3} x+y=8$

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Class 11

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Straight Lines

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Slope of line, Equation of line in different forms

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The equation of the line,where the length of the perpendicular segment from the origin to the line is $4$ and the inclination of this perpendicular segment with the positive direction of the $X$-axis is $30^{\circ}$,is:

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Find the equation of the line passing through the point $(2,2)$ and cutting off intercepts on the axes whose sum is $9$.

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