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

Solution:

The equation of the given line is √3x + y + 2 = 0

This equation can be reduced as

√3x + y + 2 = 0

⇒ - √3x - y = 2

On dividing both sides by √(-√3)² + (-1)² = 2, we obtain

⇒ - √3/2 x - 1/2 y = 2/2

⇒ (- √3/2) x + (-1/2) y = 1 ....(1)

On comparing equation (1) to x cos θ + y sin θ = p , we obtain

cosθ = - √3/2, sinθ = -1/2 and p = 1

Since the value of sin θ and cos θ are negative θ = π + π/6 = 7π/6

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

NCERT Solutions Class 11 Maths Chapter 10 Exercise ME Question 2

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

Summary:

If the equation x cos θ + y sin θ = p is the normal form of the line √3x + y + 2 = 0 then the values of θ and p are 7π/6 and 1. respectively