The parametric equations of the curve are
And 
Slope of tangent at point 
= 
Slope of normal at any point 
= 
And Equation of normal at any point
i.e., at = 
is 
Distance of normal from origin (0, 0)
= 
which is a constant.
Show that the normal at any point θ to the curve x = a cosθ + a θ sin θ, y = a sinθ – aθ cosθ is at a constant distance from the origin.
Show that the normal at any point θ to the curve x = a cosθ + a θ sin θ, y = a sinθ – aθ cosθ is at a constant distance from the origin.