. . Identifying the conics from the general equation of the conic Ax Bxy Cy Dx Ey F = . The graph of the second degree equation is one of a circle, parabola, an ellipse, a hyperbola, a point, an empty set, a single line or a pair of lines.
When, ( ) A C B D h E k F h the general equation reduces to h , which is a circle. ( ) B = and either A or C = , the general equation yields a parabola under study, at this level. ( ) A C ¹ and A and C are of the same sign, the general equation yields an ellipse. ( ) A C ¹ and A and C are of opposite signs, the general equation yields a hyperbola ( ) A C and B D E F = , the general equation yields a point x ntersecting Lines Lines ntersec sec s ec sec e c se e s ec s ec ec ec s ec s ec sec e c s ec se e c sec c ec s ec ec e sec e c sec c sec c e c sec c e c s e c se e c e c ting ting ing ng ting t ing ting ting ting ting ting ting ting ting ing n ing ing ting ting ing tin n g g ting ting tin in ing i n ing ting t i tin ng n g t i n g t in i g t i ti i n g ting t i ti tin g L Single Line Sing ng n g ng n g ng ng ng ng n g n g n g n g ng n g n g ng g ng g n g ng ng ng ng g ng ng ng n g g n g n g n g n g le L le L le L le L L e L le L L le L le L e L L le L le L le e L le L