Question

Show that the normal at any point θ to the curve

is at a constant distance from the origin.

Answer 1

We have x = a cos θ + a θ sin θ.

∴ Slope of the normal at any point θ is.

The equation of the normal at a given point (x, y) is given by,

Now, the perpendicular distance of the normal from the origin is

Hence, the perpendicular distance of the normal from the origin is constant.