Question

Question 2 Find the values of θ and p, if the equation xcosθ + ysinθ = p is the normal form of the line 3^0.5x + y + 2 = 0.

Class X1 - Maths -Straight Lines Page 233

Answer 1

Here,
equation of line is √3x + y +2 = 0

Now,
√3x + y + 2 = 0
√3x + y = -2
-√3x - y = 2

Now, divide the above equation by √{√3²+1²} both sides,

-√3x/√{√3²+1²} - y/√{√3²+1²+} = 2/√{√3²+1²}

-√3x/2 -y/2 = 2/2

-√3x/2 - y/2 = 1

(-√3/2)x + (-1/2)y = 1

we know,
Sin(210°)=sin(180°+30°)=-sin30°=-1/2

also cos(210°)=cos(180°+30°)=-cos30°=-√3/2

Use this above .

cos(210°)x + sin(210°)y = 1

Now, compare this equation to
xcos∅ + ysin∅ = P
we get ∅ = 210° and P = 1