Chapter 4: Conics Application 116
Drawing a Circle
There 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
= R
2
• The other form is the general form, which allows you to specify the coefficients of each term:
Ax
2
+ Ay
2
+ Bx + Cy + D = 0
Drawing an Ellipse
You can use the standard equation
(
− H)
2
A
2
+ = 1
(
− K)
2
B
2
to draw an ellipse.
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
A
2
– = 1
( − K)
2
B
2
• The standard form of a hyperbola with a vertical axis is:
( − K)
2
A
2
– = 1
( − H)
2
B
2
Drawing a General Conics
Using the conics general equation Ax
2
+ Bxy + Cy
2
+ 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).
