The reverse $k$ nearest neighbor query finds all points that have the query point as one of their $k$ nearest neighbors, where the $k$NN query finds the $k$ closest points to its query point. Based on conics, we propose an efficent R$k$NN verification method. By using the proposed verification method, we implement an efficient R$k$NN algorithm on VoR-tree, which has a computational complexity of $O(k^{1.5}\cdot log\,k)$. The comparative experiments are conducted between our algorithm and other two state-of-the-art R$k$NN algorithms. The experimental results indicate that the efficiency of our algorithm is significantly higher than its competitors.