Question

Show that the normal at any point 6, to the curve x = a cosθ + aθsinθ ,y = asinθ – aθcosθ is at a constant distance from the origin.

Answer 1

y – (a sinθ – a θ cosθ) 

= – cotθ(x – a cosθ – aθsinθ)

y + x cotθ = acotθcosθ + aθcotθsinθ – aθcosθ

x cosθa cos²θ, a sin²θ 

normal form is x cos θ + y sin θ = p when p is the normal from the normal to the given curve is at a consistent distance ‘a’ from the origin.