Adding Hyperbola Layers

Graph of a hyperbola with two branches. The branches approach the asymptotes y = -5 and y = 5 as x approaches positive and negative infinity, respectively. The x-axis goes from -10 to 10 and is labeled "X". The y-axis goes from -10 to 10 and is labeled "Y".

To add a hyperbola to a Cartesian graph:

  1. Insert a Cartesian graph or edit an existing graph by double-clicking it. The Cartesian Graph dialog box opens.

  2. In the Layers section, click Add.

  3. Select Hyperbola in the Add Cartesian Layer dialog box and then click OK.

  4. Choose a hyperbola type. The hyperbola can open east-west or north-south, and centered on the origin or on an arbitrary point.
    - Choose x2 ⁄ a2 - y2 ⁄ b2 = 1 to create a hyperbola that opens east-west and is centered on the origin.
    - Choose (x - h)2 ⁄ a2 - (y - k)2 ⁄ b2 = 1 to create a hyperbola that opens east-west and is centered on a point other than the origin.
    - Choose y2 ⁄ a2 - x2 ⁄ b2 = 1 to create a hyperbola that opens north-south and is centered on the origin.
    - Choose (y - h)2 ⁄ a2 - (x - k)2 ⁄ b2 = 1 to create a hyperbola that opens north-south and is centered on a point other than the origin.

  5. Enter values for the semimajor axis (a) and the semiminor axis (b).

  6. If the hyperbola is not centered on the origin, enter values for the center (h, k).

  7. Enter the Domain of the function. The default domain is from -Inf to Inf.

  8. Select a Line Style for the line.

  9. Select a Line Color.

  10. Select a Relation to specify how shading is applied to the graph.

    Relation Shading
    = The lines are shaded.
    < The area between the curves are shaded.
    <= The lines and the area between the curves are shaded.
    > The areas within the curves are shaded.
    >= The lines and areas within the curves are shaded.

  11. Click Fill Color to specify the color of the shaded area of the graph.

  12. Click Fill Shading to specify the pattern applied to the shaded area of the graph.

  13. If you want the layer to display only if a certain condition is met, enter an equation or a variable that evaluates to true or false into the Show if field. .

    Note: When entering variables, enclose the variable name in two opening and two closing number signs (for example, ##var1## = 3). The variable you reference must be defined for the question or the preface associated with the question.

  14. Click OK.