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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
y
(
– H)
2
+ (
– K)
2
= R
• The other form is the general form, which allows you to specify the parameters of each term:
x
2
y
2
x
y
A
+ A
+ B
+ C
+ D = 0
Drawing an Ellipse
You can use the standard equation
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:
• The standard form of a hyperbola with a vertical axis is:
Drawing a General Conics
Using the conics general equation A
whose principal axis is not parallel either to the
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 for a given
• 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
y
•
-intercept /
-intercept ...............................................................G-Solve -
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 38).
2
[
2
(
− H)
+
2
A
x
2
xy
+ B
+ C
y
-coordinate ................................................................. G-Solve -
x
-coordinate ................................................................. G-Solve -
\
2
(
− K)
= 1
to draw an ellipse.
2
B
[
2
(
− H)
–
A
2
\
(
− K)
2
(
–
2
A
y
2
x
y
+ D
+ E
+ F = 0, you can draw a parabola or hyperbola
x
y
-axis or the
-axis, a slanted ellipse, etc.
\
2
(
− K)
= 1
B
2
[
− H)
2
= 1
2
B
x
-Cal/
x
-Cal/
x
-Intercept / G-Solve -
Chapter 4: Conics Application 120
y
x
-Cal -
-Cal
y
y
-Cal -
-Cal
y
-Intercept
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