Location problems form an important class of combinatorial optimization problems, where we are given a set of n vertices representing locations and the goal is to pick some locations to satisfy some optimization objective. In this paper, we study three prominent problems in the location theory: k-center, k-supplier and k-dispersion problems, where k-supplier is a generalization of k-center. All three problems admit tight polynomial-time constant-approximations on metric graphs, where the distances between vertices satisfy the triangle inequality, while on general graphs, none can be approximated in polynomial time within a factor of \(\rho (n)\) for any computable function \(\rho \) . Motivated by different approximability for metric and non-metric cases, we focus on two parameters \(\alpha \) and \(\beta \) measuring the distance from a general graph to a metric graph, where \(\alpha \) is the number of vertices that appear in the triangles, in which distances violate the triangle inequality, and \(\beta \) is the minimum number of vertices, whose removal from a given graph results in a metric graph. It always holds that \(\beta \le \alpha \) . We obtain the following results: (1) A tight 3-approximation in \(O(2^\alpha \cdot n^5)\) time and a 13-approximation in \(\beta ^{O(\beta )} \cdot \mathrm{{poly}}(n)\) time for k-supplier; (2) A tight 1/2-approximation in \(O(3^\beta \cdot n^4)\) time for k-dispersion. Since k-center is a special case of k-supplier, our results imply two FPT approximation algorithms for k-center, parameterized by \(\alpha \) or \(\beta \) , which achieve approximation factors of 3 and 13, respectively. To our best knowledge, these algorithms are the first FPT constant-approximation algorithms for all three problems on general graphs parameterized by \(\alpha \) or \(\beta \) .