Q. 84.1( 82 Votes )

# In Exercises, 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^{o}.

Answer :

We know that the equation of the line having normal distance p from the origin and angle ω which the normal makes with the positive direction of x-axis is given by x cos ω + y sin ω = p.

Given p = 5 and ω = 30°

Substituting the values in the equation, we get

⇒ x cos30° + y sin30° = 5

⇒ x(√3 / 2) + y( 1/2 ) = 5

⇒ √3 x + y = 5(2) = 10

⇒ √3 x + y – 10 = 0

Ans. The equation of the line is √3 x + y – 10 = 0.

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