The length of the perpendicular segment from the origin to a line is 2 units and the inclination of this perpendicular is ∝ such that sin ∝ = and ∝ is acute. Find the equation of the line.

To Find: The equation of the line .

Given : p=2 units and = .

Since sin ∝ = =

Using Pythagoras theorem :

adj = = = 2 units.

i.e; cos ∝ = =

Formula used:

equation of the line: x cos ∝ +y sin ∝ =p

x () +y ( ) = 2

Hence ,2 x + y = 6 Or x +y =6 is the required equation of the line.