An analogue VLSI design which computes Radial Basis Function (RBF) and Multilayer Perceptron (MLP) propagation rules on a single chip is proposed to form a Conic Section Function Network (CSFN) synapse and neuron. This novel VLSI circuit has been designed to compute both the dot product (weighted sum) for MLP and the Euclidean distance for RBF. These two propagation rules are then aggregated to use for a conic section function network (CSFN) synapse and neuron design. This network allows the use of bounded and unbounded decision regions, depending on the data distribution of a given application. The cdsSpice simulation results are also presented, which verifies the function of the designed synapse and neuron.