• Sketch graphs of conic sections and write equations related to conic sections.

• Graphs will be selected from the circle, ellipse, parabola and hyperbola. Completion of the square may be required.

• Appropriate features must be indicated, for example: asymptotes and intercepts.

• Equations may be in Cartesian or parametric form.

• Writing equations will be for a given graph of a conic section.

• Solve problems involving conic sections.

• Problems involving modelling with conic sections may include contexts such as: bridges, cross sections of tunnels, profiles of shadows formed by light shades, ovals, cross sections of punchbowls.

• Problems may involve finding:

  • equations of tangents or normals

  • points of intersection between lines and conics.

Note: implicit or parametric differentiation may be required to find equations of tangents or normals.

• Solve more complex conic section problems.

• Problems may involve:

  • a proof

  • a chain of reasoning

  • loci

  • knowledge of eccentricity or directrix.