Find the equation of the straight line passing through (3, -2) an… - Vidyadip

Question

Find the equation of the straight line passing through $(3, -2)$ and making an angle of 60° with the positive direction of y-axis.

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Answer

The required equation of the line is $y-y_1=m\left(x-x_1\right)$ Since the lline makes an angle $60^{\circ}$ with the positive direction of $y$-axis, it makes $30^{\circ}$ with the positive direction of $x$-axis. $\therefore m=\tan 30^{\circ}=\frac{1}{\sqrt{3}}$ (angle with $y$-axis) A point on the line is $\left(\mathrm{x}_1 \mathrm{y}_1\right)=(3,-2)$ Therefore, the equation of the line is: $\mathrm{y}-\mathrm{y}_1=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_1\right) \mathrm{y}-(-2)=\frac{1}{\sqrt{3}}(\mathrm{x}-3)$
$x-\sqrt{3} y-3-2 \sqrt{3}=0$

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