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  • Find the equation of the line which satisfy the given conditions: (6) Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30 degree with positive direction of the x-axis.

Find the equation of the line which satisfy the given conditions: 

Q : 6         Intersecting the y-axis at a distance of 2 units above the origin and making an angle of  30^{\circ} with positive direction of the x-axis. 

Answers (1)

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We know that , equation of line passing through point (x_1,y_1) and with slope m is given by
(y-y_1)=m(x-x_1)
Line Intersecting the y-axis at a distance of 2 units above the origin which means point is (0,2)
we know that
m = \tan \theta\\ m = \tan 30\degree \ \ \ \ \ \ \ \ \ \ \ \ \ (\because \theta = 30 \degree \ given)\\ m = \frac{1}{\sqrt3}
Now, the equation of the line passing through the point (0,2) and with slope \frac{1}{\sqrt3}  is 
(y-2)= \frac{1}{\sqrt3}(x-0)\\ \sqrt3(y-2)= x\\ x-\sqrt3y+2\sqrt3=0
Therefore, the equation of the line  is   x-\sqrt3y+2\sqrt3=0

Posted by

Gautam harsolia

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