Abstract: Green's function method is an important way to solve the modern physical problems. The wave equation, the diffusion equation, the Helmholtz equation, the Poisson equation, which is one of the important equations to describe the steady field, and many problems in modern engineering can be solved by using Green's function method. For the first boundary value problem of Poisson equation, most of the research only gives the Green's function solution to the areas with ellipsoidal surface or spherical surface and so on, but there is little discussion on other types of areas. Based on the quadratic surface imaging formula, the first boundary value problem of the Poisson equation in the areas with quadratic surfaces such as ellipsoid, hyperboloid, paraboloid and sphere is studied uniformly in this text by using electric image method. The purpose is to give the Green's function.

Key words: Rotational conicoid, Focus, Method of electric image, Green's function