Given, assuming that both A and C are non-zero, then the graph of \(\displaystyle{A}{x}^{{{2}}}+{C}{y}^{{{2}}}+{D}{x}+{E}{y}+{F}={0}\) can represents any of the conic sections. We have to check whether the statement is true of not.
Since the general form of the conic is \(\displaystyle{A}{x}^{{{2}}}+{C}{y}^{{{2}}}+{D}{x}+{E}{y}+{F}={0}\) If both A and C are zero then the equation of the section becomes linear which is a contradiction. The equation of a conic section is quadratic. Hence if the values of A and B are non-zero then the graph of \(\displaystyle{A}{x}^{{{2}}}+{C}{y}^{{{2}}}+{D}{x}+{E}{y}+{F}={0}\) can represent any of the conic sections.
Hence the statement is true.