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asked 2021-08-10

Let A be a symmetric \(\displaystyle{2}\times{2}\) matrix and let k be a scalar. Prove that the graph of the quadratic equation \(\displaystyle{x}^{{T}}\) Ax=k is ,an ellipse, circle, or imaginary conic if \(\displaystyle{k}\ne{q}{0}\) and det A > 0

asked 2020-10-21

Determine whether the statement, 'I noticed that depending on the values for A and C, assuming that they are not both zero, the graph of \(\displaystyle{A}{x}^{{{2}}}+{C}{y}^{{{2}}}+{D}{x}+{E}{y}+{F}={0}\) can represent any of the conic sections', makes sense or does not make sense, and explain your reasoning.

asked 2021-08-09

Show that the equation represents a conic section. Sketch the conic section, and indicate all pertinent information (such as foci, directrix, asymptotes, and so on). \(\displaystyle{\left({a}\right)}{x}^{{2}}–{2}{x}–{4}{y}^{{2}}–{12}{y}=-{8}{\left({b}\right)}{2}{x}^{{2}}+{4}{x}-{5}{y}+{7}={0}{\left({c}\right)}{8}{a}^{{2}}+{8}{x}+{2}{y}^{{2}}–{20}{y}={12}\)

asked 2021-08-07

Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}},{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\)?. For hyperbola, find the asymptotes. Sketch the graph. \(\displaystyle{9}{x}^{{2}}-{y}^{{2}}+{36}{x}+{4}{y}+{23}={0}\)

asked 2021-08-09

Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}},{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\)?. For hyperbola, find the asymptotes. Sketch the graph. \(\displaystyle{y}^{{2}}+{4}{y}-{2}{x}+{6}={0}\)

asked 2021-08-11

Find the equation of the graph for each conic in standard form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}},{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\)?. For hyperbola, find the asymptotes. Sketch the graph. \(\displaystyle{9}{x}^{{2}}+{25}{y}^{{2}}+{54}{x}-{50}{y}-{119}={0}\)

asked 2021-08-11

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}}\), \(\displaystyle{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\). For hyperbola,find the asymtotes.Sketch the graph

\(\displaystyle{16}{x}^{{2}}-{4}{y}^{{2}}-{64}={0}\)

\(\displaystyle{16}{x}^{{2}}-{4}{y}^{{2}}-{64}={0}\)