Casio FXCP400 4-3Using G-Solveto Analyze a Conics Graph, − H), − K), − K), − H), G-Solve- Focus, G-Solve- Vertex, G-Solve- Center, G-Solve- Radius, Drawing a Circle

Drawing a CircleThere are two forms that you can use to draw a circle.

•One form is the standard form, which allows you to specify the center point and radius: (x – H)2 + (y – K)2 = R2

•The other form is the general form, which allows you to specify the coefficients of each term: Ax2 + Ay2 + Bx + Cy + D = 0

Drawing an EllipseYou can use the standard equation ( − H)2 + ( − K)2 = 1 to draw an ellipse.

A2B2

Drawing a Hyperbola

A hyperbola can be drawn with either a horizontal or vertical orientation. The hyperbola type is determined by the direction of its principal axis.

• The standard form of a hyperbola with a horizontal axis is: ( − H)2 – ( − K)2 = 1

A2B2

•The standard form of a hyperbola with a vertical axis is: ( − K)2 – ( − H)2 = 1

A2B2

Drawing a General Conics

Using the conics general equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, you can draw a parabola or hyperbola whose principal axis is not parallel either to the x-axis or the y-axis, a slanted ellipse, etc.

4-3 Using G-Solve to Analyze a Conics Graph

What You Can Do Using the G-Solve Menu Commands

While there is a graph on the Conics Graph window, you can use a command on the [Analysis] - [G-Solve] menu to obtain the following information.

• x-coordinate for a given y-coordinate.................................................................	G-Solve - x-Cal/y-Cal - x-Cal
• y-coordinate for a given x-coordinate.................................................................	G-Solve - x-Cal/y-Cal - y-Cal
• Focus of a parabola, ellipse, or hyperbola .............................................................................	G-Solve - Focus
• Vertex of a parabola, ellipse, or hyperbola ...........................................................................	G-Solve - Vertex
• Directrix of a parabola........................................................................................................	G-Solve - Directrix
• Axis of symmetry of a parabola.......................................................................................	G-Solve - Symmetry
• Length of the latus rectum of a parabola ......................................................	G-Solve - Latus Rectum Length
• Center point of a circle, ellipse, or hyperbola........................................................................	G-Solve - Center
• Radius of a circle .................................................................................................................	G-Solve - Radius
• Asymptotes of a hyperbola ...........................................................................................	G-Solve - Asymptotes
• Eccentricity of a parabola, ellipse, or hyperbola ...........................................................	G-Solve - Eccentricity
• x-intercept / y-intercept ...............................................................	G-Solve - x-Intercept / G-Solve - y-Intercept

Tip: The color of Directrix, Symmetry, Asymptotes lines drawn using G-Solve is the color specified by the Graph Format Sketch Color. For more information about Graph Format, see “Graph Format Dialog Box” (page 36).

Chapter 4: Conics Application 116