Q : 14 . Find equation of the line through the point making an angle with the positive -axis. Also, find the equation of line parallel to it and crossing the -axis at a distance of units below the origin.

Name: Find equation of the line through the point (0, 2) making an angle 2π/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
Uploaded: Tue, 2019-06-11 16:05
Description: Find equation of the line through the point (0, 2) making an angle 2π/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Find equation of the line through the point (0, 2) making an angle 2π/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

Q : 14 . Find equation of the line through the point $(0,2)$ making an angle $\frac{2\pi }{3}$ with the positive $x$ -axis. Also, find the equation of line parallel to it and crossing the $y$ -axis at a distance of $2$ units below the origin.

Answers (1)

We know that
$m = \tan \theta \\ m = \tan \frac{2\pi}{3} = -\sqrt3$
Now, equation of line passing through point (0 , 2) and with slope $-\sqrt3$ is
$(y-2)= -\sqrt3(x-0)\\ \sqrt3x+y-2=0$
Therefore, equation of line is $\sqrt3x+y-2=0$ -(i)

Now, It is given that line crossing the $y$ -axis at a distance of $2$ units below the origin which means coordinates are (0 ,-2)
This line is parallel to above line which means slope of both the lines are equal
Now, equation of line passing through point (0 , -2) and with slope $-\sqrt3$ is
$(y-(-2))= -\sqrt3(x-0)\\ \sqrt3x+y+2=0$
Therefore, equation of line is $\sqrt3x+y+2=0$

Posted by

Gautam harsolia

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Q : 14 . Find equation of the line through the point making an angle with the positive -axis. Also, find the equation of line parallel to it and crossing the -axis at a distance of units below the origin.

Answers (1)

Posted by

Gautam harsolia

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Q : 14 . Find equation of the line through the point $(0,2)$ making an angle $\frac{2\pi }{3}$ with the positive $x$ -axis. Also, find the equation of line parallel to it and crossing the $y$ -axis at a distance of $2$ units below the origin.