Students will identify, analyze, and sketch the graphs of the conic sections and relate the equations and graphs.
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Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers
Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; find the equations for the asymptotes of a hyperbola
Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section
Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate
Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology