The Euclidean Distance Degree (EDD) of a variety is the number of critical points of the squared distance function of a general point outside the variety. In this thesis we give a classification of conics based on their EDD, originally attributed to Cayley. We show that circles and parabolas have EDD 2 and 3 respectively while all other conics have EDD 4. We reduce the computation of the EDD to finding solutions of the determinant of a certain generalized matrix, called the hyperdeterminant of type 2 × 3 × 3. This determinant is computed using the celebrated Schläfli decomposition.