Curvature of the Focal Conic in the Isotropic Plane

It is shown in {beba} that every focal conic C in the isotropic plane can be represented by the equation y²=ε x²+x, ε ∈ \-1,0,1\ and a parametrization. This paper gives the equation of the circle of curvature at the point T of the focal conic C. The radius of curvature ρ at the point T of the focal conic C is given as well as its relation to the span δ from the center of C to the tangent at the point T and to the length of the half diameter of C on the diameter parallel to the tangent. 2000 Mathematics Subject Classification. 51N25