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Precalculus » J. Analytic Geometry

  • J.1. Parabolas

    1. J.1.M. Play Multiplayer 0 wins, 0 losses

    2. J.1.Q. Unit Challenge

    3. J.1.1. Standard Form of the Equation of a Parabola with Vertex at the Origin

      1. J.1.1.O. Overview
      2. J.1.1.1. Find the standard form of the equation of a parabola given a focus
      3. J.1.1.2. Find the standard form of the equation of a parabola given a directrix
      4. J.1.1.3. Find the standard form of the equation of a parabola given an axis and a point on the parabola

    4. J.1.2. Vertex, Focus, and Directrix

      1. J.1.2.O. Overview
      2. J.1.2.1. Find the vertex given an equation
      3. J.1.2.2. Find the focus given an equation
      4. J.1.2.3. Find the directrix given an equation
      5. J.1.2.4. Find the directrix given an equation

    5. J.1.3. Standard Form of the Equation of any Parabola

      1. J.1.3.1. Find the standard form of the equation of a parabola given a vertex and focus
      2. J.1.3.2. Find the standard form of the equation of a parabola given a vertex and directrix focus
      3. J.1.3.3. Find the standard form of the equation of a parabola given a focus and directrix
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  • J.2. Ellipses

    1. J.2.M. Play Multiplayer 0 wins, 0 losses

    2. J.2.Q. Unit Challenge

    3. J.2.1. Standard Form of the Equation of an Ellipse with Center at the Origin

      1. J.2.1.O. Overview
      2. J.2.1.1. Find the standard form of the equation of the ellipse given the vertices and foci
      3. J.2.1.2. Find the standard form of the equation of the ellipse given the foci and major axis
      4. J.2.1.3. Find the standard form of the equation of the ellipse given the vertices and a point on the ellipse

    4. J.2.2. Standard Form of the Equation of any Ellipse

      1. J.2.2.O. Overview
      2. J.2.2.1. Find the standard form of the equation of the ellipse given vertices and minor axis
      3. J.2.2.2. Find the standard form of the equation of the ellipse given foci and major axis
      4. J.2.2.3. Find the standard form of the equation of the ellipse given center, vertex, and minor axis

    5. J.2.3. Center, Radius, Vertices, Foci, and Eccentricity

      1. J.2.3.O. Overview
      2. J.2.3.1. Find the center of an ellipse given an equation
      3. J.2.3.2. Find the vertices of an ellipse given an equation
      4. J.2.3.3. Find the foci of an ellipse given an equation
      5. J.2.3.4. Find the eccentricity of an ellipse given an equation
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  • J.3. Hyperbolas

    1. J.3.M. Play Multiplayer 0 wins, 0 losses

    2. J.3.Q. Unit Challenge

    3. J.3.1. Center, Vertices, Foci, and Asymptotes

      1. J.3.1.O. Overview
      2. J.3.1.1. Find the center of a hyperbola given an equation
      3. J.3.1.2. Find the vertices of a hyperbola given an equation
      4. J.3.1.3. Find the foci of a hyperbola given an equation
      5. J.3.1.4. Find the equations of the asymptotes of a hyperbola

    4. J.3.2. Standard Form of the Equation of a Hyperbola with Center at the Origin

      1. J.3.2.O. Overview
      2. J.3.2.1. Find the standard form of the equation of a hyperbola given vertices and foci
      3. J.3.2.2. Find the standard form of the equation of a hyperbola given vertices and asymptotes
      4. J.3.2.3. Find the standard form of the equation of a hyperbola given foci and asymptotes

    5. J.3.3. Standard Form of the Equation of any Hyperbola

      1. J.3.3.O. Overview
      2. J.3.3.1. Find the standard form of the equation of a hyperbola given vertices and foci
      3. J.3.3.2. Find the standard form of the equation of a hyperbola given vertices and a point on the hyperbola
      4. J.3.3.3. Find the standard form of the equation of a hyperbola given vertices and asymptotes
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  • J.4. Rotation of Conics

    1. J.4.M. Play Multiplayer 0 wins, 0 losses

    2. J.4.Q. Unit Challenge

    3. J.4.1. Classifying Conic Sections

      1. J.4.1.O. Overview
      2. J.4.1.1. Classify the graph of the equation as a circle, parabola, ellipse, or hyperbola given a general equation
      3. J.4.1.2. Use the discriminant to classify the graph as a parabola, ellipse, or hyperbola

    4. J.4.2. Rotation

      1. J.4.2.O. Overview
      2. J.4.2.1. Find the coordinates of the point in the rotated coordinate system
      3. J.4.2.2. Rotate the axes of a hyperbola to eliminate the xy-term and then write the equation in standard form
      4. J.4.2.3. Rotate the axes of an ellipse to eliminate the xy-term and then write the equation in standard form
      5. J.4.2.4. Rotate the axes of a parabola to eliminate the xy-term and then write the equation in standard form
      6. J.4.2.5. Sketch the graph of the rotated conic
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  • J.5. Parametric Equations

    1. J.5.M. Play Multiplayer 0 wins, 0 losses

    2. J.5.Q. Unit Challenge

    3. J.5.1. Parametric Equations

      1. J.5.1.O. Overview
      2. J.5.1.1. Sketch the curve represented by the parametric equations, including the orientation of the curve
      3. J.5.1.2. Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve
      4. J.5.1.3. Find a set of parametric equations to represent the equation for the graph
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  • J.6. Polar Equations of Conics

    1. J.6.M. Play Multiplayer 0 wins, 0 losses

    2. J.6.Q. Unit Challenge

    3. J.6.1. Polar Equations of Conics

      1. J.6.1.O. Overview
      2. J.6.1.1. Write the polar equation of the conic given an eccentricity for the conic and identify the conic for each equation
      3. J.6.1.2. Identify the conic and sketch its graph
      4. J.6.1.3. Find the polar equation of the conic with its focus at the pole given the eccentricity and directrix
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