An example of the geometry of a 5th-order ODE: the metric on the space of conics in {mathbb{CP}}²

As an application of the method of [4], we find the metric and connection on the space of conics in $\mathbb{CP}^2$ determined as the solution space of the ODE eqn(1). These calculations underpin the twistor construction of the Radon transform on conics in $\mathbb{CP}^2$ described in [5]. Two further examples of the method are provided.