Question

Find the values of θ and p, if the equation  x cosθ + y sinθ =p is the normal form of the line √ 3x + y + 2=0.

Answer 1

The equation of the given line is  √3x + y + 2=0.
This equation can be reduced as

Comparing equation (1) to x cosθ + y sinθ = p , we obtain

Since the values of sin θ and cos θ are negative,

Thus, the respective values of θ and p are 7π/6 and 1.