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

Find the equation of the line which satisfy the given conditions. Passing through (1,1) and (5,4)

Find the equation of the st. line, which has length of perpendicular segment from the origin to the line 4 units and the inclination of the perpendicular segment with the positive direction of x-axis is 30^@ .

Find the equation of the family of lines satisfying the following condition : passing through the origin .

Find the equation of the plane given that the foot of perpendicular drawn from the origin into the plane is (1,2,3).

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.:- x-y= 4.

Reduce the following to the normal form. Find their perpendicular-distances from the origin and angle between perpendicular and the positive x-axis. x-y=4 .

Reduce the following to the normal form. Find their perpendicular-distances from the origin and angle between perpendicular and the positive x-axis. y-2=0 .

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.:- x-sqrt3 y+8=0