Question

Reduce the equations into normal form, find their perpendicular distances from the origin and angle between perpendicular and the possible x-axis.

(i) x - √3y + 8 = 0

(ii) y - 2 = 0

(iii) x - y = 4

(iv) √3x + y - 8 = 0

Answer 1

(ii) Given : y – 2 = 0

y=2 ⇒ o.x +1.y = 2 

Compare with x cos(ω) + y sin(ω) = p 

we get, cos(ω) = 0, sin(ω) = 1, p = 2 

we know that, 

cos(90°) = 0 and sin(90°) = 1 

ω = 90° and p = 2 

∴ Required normal form is, 

x cos(90°) + y sin(90°) = 2