=aθsinθ...(2) From equations (1) and (2), we get
dy
dx
=tanθ⇒ Slope of normal =−cotθ Equation of normal at ′θ′ is y−a(sinθ−θcosθ) =−cotθ(x−a(cosθ+θsinθ) ⇒ysinθ−asin2θ+aθcosθsinθ =−xcosθ+acos2θ+aθsinθcosθ ⇒xcosθ+ysinθ=a Clearly this is an equation of straight line - which is at a constant distance a′ from origin.