Question

Find the value of θ and P, if the equation x cosθ + y sin theta = p is the normal form if the line √3x +y +2 =0

please tell fast

Answer 1

Answer:

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

this equation can be reduced as −3x−y=2

on dividing both sides by (−3)2+(−1)2=2,

we obtain −23x−21y=22

⇒{−23}x+{−21}y=1....(1)

On comparing equation (1) to xcosθ+ysinθ=p,

we obtain cosθ=−23,sinθ=−21, and p=1

Since the value of sinθ  and cosθ  are both negative,  θ is  in the third quadrant 

 ∴θ=π+6π=67π