Q. 84.8( 6 Votes )

# Find the value of θ and p if the equation x cos θ + y sin θ = p is the normal form of the line .

Answer :

**Given:** the normal form of a line is x cos θ + y sin θ = p …..… (1)

**To find:**

P and θ.

**Explanation:**

Let us try to write down the equation √3 + y + 2 = 0 in its normal form.

Now √3 + y + 2 = 0

⇒ √3 + y = – 2

Dividing both sides by 2,

⇒ – √3/2 – y/2 = 1

…… (2)

Comparing equations (1) and (2) we get,

and p = 1

⇒ θ = 210° = 7π/6 and p = 1

**Hence**, θ = 210° = 7π/6 and p = 1

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