First slide

Equation of line in Straight lines

Question

A straight line makes an angle $\frac{π}{3}$ with positive direction of x-axis measured in anti clock direction and makes positive intercept on y-axis and the line is at a distance of 5 units from origin then its equation is

Easy

A

$y = \sqrt{3} x - 10$
B

$y = \sqrt{3} x + 10$
C

$y = \sqrt{3} x + 8$
D

$y = \sqrt{3} x - 8$

Solution

$α = 150^{0}, p = 5$
$x \cos α + y \sin α = p$
$\Rightarrow x (- \frac{\sqrt{3}}{2}) + y (\frac{1}{2}) = p$
$\Rightarrow y = \sqrt{3} x + 10$

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