Question

The length of the perpendicular drawn from the origin to a line is 12 and makes an angle 150◦ with positive direction of the x-axis. Find the equation of the line.​

Answer 1

Answer:

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Answer 2

$\mathsf{ \star \: Length \: of \: the \: perpendicular \: line \: (P)=12}$

And,

Let us consider the given angle as,

$\boxed{ \mathtt{ \theta = 150 \degree}}$

We know that,

$\boxed{ \color{blue} \mathsf{⇒x \: cos \: \theta + y \: sin \: \theta = p}}$

Replace the value of θ = 150:

$\mathsf{⇒x \: cos \: 150 \degree + y \: sin \: 150 \degree = 12}$

$\mathsf{⇒x[cos \: (180 \degree - 30 \degree)]+ y[sin(180 \degree - 30 \degree)] = 12}$

$\mathsf{⇒ [- cos \: 30 ]+ y \: sin \: 30 \: = 12}$

$\mathsf{⇒x( \frac{ - \sqrt{3} }{2} ) + y( \frac{1}{2} ) = 12}$

Taking L.C.M:

$\mathsf{⇒ - \sqrt{3} x + y = 24}$

Required Answer:

$\boxed{ \color{red}\mathsf{ \sqrt{3} x - y + 24 = 0}}$