# The Kappa Curve as a Locus

The Kappa Curve as a Locus

The kappa curve looks vaguely like a curly kappa, , and was studied by Newton, Bernoulli, and Gutschoven. Sometimes called Gutschoven's curve, its double cusp form can be represented as +=.

ϰ

2

y

2

x

2

y

2

a

2

x

Let be the point (magenta). Let be the intersection point (blue) of the horizontal line with a line rotating about the origin . The kappa curve is the locus of points (red) on the rotating line such that distances (green segments).

R

(0,a)

S

y=a

y=xtan(θ)

O

P

OP=RS