In this talk, we study the paper "Coordinate shadows of semi-definite and Euclidean distance matrices" by D. Drusvyatskiy, G. Pataki and H. Wolkowicz. They investigate geometry properties of the projection of the semi-definite and Euclidean distance cones onto a subset of the matrix entries. Their results elucidate the Krislock-Wolkowicz facial reduction algorithm. For example, combinatorial characterizations of the "minimal cones" of certain problems can be derived under a chordality assumption. Therefore, they also established a connection between singularity degree and the exposedness of conic images under a linear mapping. We will try to cover the main ideas in this paper, as well as some technical details.