Today's society expects schools to ensure that all students have an opportunity to become mathematically literate....

NCTM Standards

sections:

      9.1, 9.2, 9.3, 9.4, 9.5, and 9.6

We now consider generalized quadratic equations in two-dimensions. These result in a family of curves which can be generated by slicing a cone.

objectives:

• identify the general quadratic equation in two variables
• explain what is meant by a conic section
• define the curve ellipse
• identify standard forms of the equation of an ellipse
• reduce a quadratic equation representing an ellipse to standard form
• calculate the foci and the eccentricity of an ellipse
• graph an ellipse
• relate the ellipse to a circle
• define the terms and use the focus and directrix
• define the curve hyperbola
• identify standard forms of the equation of a hyperbola
• reduce a quadratic equation representing a hyperbola to standard form
• calculate the foci of a hyperbola
• graph a hyperbola
• define the curve parabola
• identify standard forms of the equation of a parabola
• reduce a quadratic equation representing a parabola to standard form
• graph a parabola
• identify conic section that contain an xy term
• discuss the rotation of the axes
• transform a conic section to eliminate the xy term

• identify a parametric equation
• graph a plane curve defined by parametric equations
• eliminate the parameter to derive a relationship between the independent and dependent variables
• discuss the advantages of one form compared to the other

• express the conic sections in polar form
• graph conic sections in polar form