Find the equation of the line where length of the perpendicular segmentfrom the origin to the line is 4 and the inclination of the perpendicular segment with thepositive direction of x-axis is 30°

y = 8 - 3 \sqrt{x}

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y = 2

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x = 2

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x = - 2

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Solution

The correct option is B $y = 8 - 3 \sqrt{x}$
The normal form of equation of the line is
$x cos u + y sin w = p .$
Here, $p = 4$ and $w = 30$

Equation of the line is $x cos 30 + y sin 30 = 4$
$\Rightarrow \frac{x \sqrt{3}}{2} + y \frac{1}{2} = 4$
$\Rightarrow \sqrt{3} x + y = 8$
$\Rightarrow y = 8 - 3 \sqrt{x}$

Hence, this is the answer.

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Find the equation of the line where length of the perpendicular segmentfrom the origin to the line is 4 and the inclination of the perpendicular segment with thepositive direction of x-axis is 30°

The correct option is B y=8−3√xThe normal form of equation of the line is xcosu+ysinw=p. Here, p=4 and w=30Equation of the line is xcos30+ysin30=4⇒x√32+y12=4⇒√3x+y=8⇒y=8−3√xHence, this is the answer.