Texas Instruments -83 Plus Silver Edion User manual

11/6/02 © 2000–2002 Texas Instruments
TI-83 Plus
Conic Graphing
Getting Started
Start here
How To…
Start and Quit Conic Graphing
Use Conic Window and Conic Zoom
Graph and Trace a Conic Section
Examples
Graphing a Circle Graphing a Hyperbola
Graphing an Ellipse Graphing a Parabola
More Information
Deleting Conic Graphing Customer Support
Error Recovery Glossary
TI

TI-83 Plus Conic Graphing Page 2
Important Information
Texas Instruments makes no warranty, either expressed or
implied, including but not limited to any implied warranties of
merchantability and fitness for a particular purpose, regarding any
programs or book materials and makes such materials available
solely on an “as-is” basis.
In no event shall Texas Instruments be liable to anyone for
special, collateral, incidental, or consequential damages in
connection with or arising out of the purchase or use of these
materials, and the sole and exclusive liability of Texas
Instruments, regardless of the form of action, shall not exceed the
purchase price of this item or material. Moreover, Texas
Instruments shall not be liable for any claim of any kind
whatsoever against the use of these materials by any other party.
Graphing product applications (Apps) are licensed. See the terms
of the license agreement for this product.
Windows, NT, Apple, and Mac are trademarks of their respective owners.

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Where to Find Installation Instructions
You can find detailed instructions on installing this and other free
Flash applications in the guides section of education.ti.com.
Follow the link to Flash Installation Instructions.
Installing this application requires TIGRAPH LINKËsoftware
and link cable. You can purchase a link cable from the online
store. After you enter the store, follow the links to Computer
Software, then TI-GRAPH LINK.
You can download a free copy of the latest version of TIGRAPH
LINK software from the software section of education.ti.com.
Follow the links to Connectivity Software, then TI-GRAPH LINK.

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What is Conic Graphing?
Conic Graphing is a TI83 Plus calculator software application
that you can use to graph the four basic conic sections. The
conic equations can be in function, parametric, and polar forms.
Conic Graphing does not address degenerate cases of conic
sections where the plane passes through the vertex resulting in a
point, line, or two intersecting lines.
Ellipse
Circle
Parabola
Hyperbola

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Starting and Quitting Conic Graphing
Starting Conic Graphing
Quitting Conic Graphing
1. Press nto display the list
of applications on your
calculator.
2. Press `or hto move the
cursor to Conics and press
¯. The CONICS main
menu is displayed.
From the CONICS main menu:
Select QUIT.
From any other screen:
Press \[QUIT].
Values you input in Conic
Graphing are saved in an
application variable (AppVar) when
you exit the application. The next
time you run the application, the
last values you entered will be
displayed.

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Getting Started
Work through this exercise to become familiar with the basic features of the Conic
Graphing application. In this exercise, you trace the trajectory of Haley’s comet.
One of the more common uses of conics is to show the orbits of
planets and other astronomical bodies. Planets have closed
orbits that are almost circular, while comets have highly elliptical
orbits. For example, Haley’s comet follows a long path out from
the sun, but passes very close to the sun when it returns to the
solar system. It has a major axis of 36.18 astronomical units, and
an eccentricity of 0.97 (Larsen, Hostetler, and Edwards. 1997,
821). You can use Conic Graphing to trace the trajectory of
Haley’s comet.
Note
To complete this exercise, you need to set your calculator to
radian mode before you start the Conics application. To do this:
1. Press ].
2. Move the cursor to Radian, and press ¯.
3. Press sto exit the mode screen.

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1. We know the following: r = 2ep
1+e sin T, e = 0.97, and
2a ≈36.18. Find p, the halfway point of the distance from the
focus to the directrix.
r1=
2
sin1
2
π
e
ep
+
r2=
2
3
sin1
2
π
e
ep
+
2a ≈36.18 ≈r1+ r2,then
36.18 ≈
2
sin1
2
π
e
ep
+
+
2
3
sin1
2
π
e
ep
+
Thus, p = .551
2. Select ELLIPSE from the CONICS main menu.
3. Press ]to display the CONIC SETTINGS screen.
4. Select POL to change the mode to polar.
5. Select Man so that you can manually change window
settings.
6. Select ESC to return to the ELLIPSE screen.
7. Press hto select equation 4, R = 2ep
1 + e sin (T).

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8. Enter these parameters for e and p, as defined above in step
1: e = 0.97, p = .551
9. Press Tto display the CONIC ZOOM screen.
10. Select Zoom Conic so that the aspect ratio on the screen is
square. The graph of the ellipse is drawn.
The center (0, S
2) is
the sun. The graph
shows the path
around the sun.
To see this graph,
press T, and
select ZStandard,
then press T,
and select ZoomIn.
Press ¯with the
cursor near the
origin.

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11. Press Rto exit the graph screen.
12. Press e?to find the foci. One focus is the sun at
distance 0, angle S
2, ≈1.5708 radians. (If the calculator is in
degree mode, the distance is 0 and the angle is 90 degrees.
To change to degree mode, you must exit Conic Graphing.)
13. Press Uto trace the trajectory.
Note
Conic Graphing does not allow for continuous tracing. For
example, after you trace the entire ellipse, the tracing stops. You
can then press the opposite direction arrow to trace the object in
the opposite direction.

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Variables Used or Modified by the Application
Conic Graphing modifies various calculator and window
variables.
•Y-vars in the list below are modified, but are not restored
when you exit the application.
•Real number variables in the list below are modified, but are
restored after you exit the application.
•If any of the variables were archived, Conic Graphing
unarchives them, but does not archive them again after you
exit the application.
Variable type
Variables used or modified
Y-vars
Parametric equation editor: X1T, Y1T, X2T, Y2T
Polar equation editor: r1
Real number
variables
A, B, C, D, E, F, G, H, J, K, L, M, N, O, P, Q, R,
S, T, U, W, X, Y, Z, T
See the TI83 Plus manual Getting Started section for more
information about variables.