Q

Find the equation of the line which satisfy the given conditions: (8) Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30 degree.

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

Q : 8         Perpendicular distance from the origin is $5$ units and the angle made by the  perpendicular with the positive $x$-axis is  $30^{\circ}$

Views

It is given that length of perpendicular is 5 units  and  angle made by the  perpendicular with the positive $x$-axis is  $30^{\circ}$
Therefore, equation of line is
$x\cos \theta + y \sin \theta = p$
In this case p = 5 and  $\theta = 30\degree$
$x\cos 30\degree + y \sin 30\degree = 5\\ x.\frac{\sqrt3}{2}+\frac{y}{2}= 5\\ \sqrt3x+y =10$
Therefore, equation of the line  is   $\sqrt3x+y =10$

Exams
Articles
Questions