Texas instruments TI-83 PLUS Conic Graphing

TI

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

11/6/02 © 2000–2002 Texas Instruments

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TI-83 Plus Conic Gr aphi ng Page 2

TI-83 Plus Conic Graphing Page 3

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 LINKË software
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.

TI-83 Plus Conic Graphing Page 4

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

TI-83 Plus Conic Graphing Page 5

Starting and Quitting Conic Graphing

Starting Conic Graphing

Quitting Conic Graphing

1. Press

n to display the list
of applications on your
calculator.

2. Press ` or h to 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 s to 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

2πe

ep

+

r2=

23sin1

2πe

ep

+

2a ≈ 36.18 ≈ r1+ r2,then

36.18 ≈

2

sin1

2πe

ep

+

+

23sin1

2πe

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

T

to 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

R

to 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

U

to 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.

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Conic Settings

You can graph conic sections in function, parametric, or polar
mode, based on your requirements. The Conic Graphing
application restores the calculator to the original mode (before
you started the application) when you exit the application.

Graphing Mode

Description
FUNC

(function)

Plots functions where Y is a function of X

PAR

(parametric)

Plots relations where X and Y are functions of
T

POL

(polar)

Plots functions where R is a function of

T

You can also select automatic or manual window settings.

•

Automatic changes the viewing window settings so that the
conic section is displayed, no matter where it is on the graph.
You cannot access window or zoom settings to change them
manually.

•

Manual allows you to change the window and zoom settings
manually. If the conic section is graphed outside of the
viewing window, you must manually change the settings so
that it will be displayed in the viewing window.

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From any Conic Graphing screen:

1. Press

]

. The

CONIC SETTINGS s

creen is displayed.

2. Press

a

or _ to highlight a graphing type mode and press

¯

to select it.

3. Press h to move to

WINDOW SETTINGS

.

4. Press a or _ to highlight AUTO (automatic) or MAN (manual)
and press

¯

to select it.

5. Press

R

to select ESC to save the settings and return to the

previous screen.

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Conic Graphing Options

Selecting Options

To select an option at the bottom of a Conic Graphing screen,
press the graphing key directly below the option.

• Select INFO to display the information screen, which contains
the application version number.

• Select QUIT to exit Conic Graphing.

• Select ESC to go back one screen.

R S T U V R S T U V

Press a
graphing
key to
select an
option.

TI-83 Plus Conic Graphing Page 14

Window and Zoom Settings

CONIC WINDOW

The

CONIC WINDOW

settings screen allows you to modify the
window characteristics. This screen is similar to the calculator’s
windowsettings screen. You can change individual window
parameters as needed.

1. Make sure that the conic graphing type mode is set correctly

(to function, parametric, or polar, depending on what the
equation requires).

2. Make sure the window settings mode is set to MAN.

3. Select a conic section from the

CONICS

main menu: CIRCLE,

ELLIPSE, HYPERBOLA, or PARABOLA.

4. Select an equation.

Note

•

You can only access the CONIC WINDOW screen after you

have selected an equation to graph.

•

You can only access the CONIC WINDOW screen if the mode

is set to MAN.

5. Set the parameters (for example, provide H, K, and Rfor the

first circle equation in function mode).

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6. Press

S

.

7. Change the window parameters as needed.

8. Press Rto return to the previous screen.

Graphing
Mode

Window
Parameter

Description

All modes

Xmin

Smallest x value to be
displayed in the viewing window

Xmax

Largest x value to be displayed
in the viewing window

Xscl

Spacing between the tick marks
on the x-axis

Ymin

Smallest y value to be displayed
in the viewing window

Ymax

Largest y value to be displayed
in the viewing window

Yscl

Spacing between the tick marks
on the y-axis

Parametric
mode

Tmin

Smallest T value (step) to
evaluate

TI-83 Plus Conic Graphing Page 16

Graphing
Mode

Window
Parameter

Description

Tmax

Largest T value to evaluate
Tstep

Step increment
Polar mode

(ellipse
equations and
circle
equations
1 and 2)

T

min

Smallest Tvalue (angle) to
evaluate in radians/degrees

T

max

Largest Tvalue to evaluate in
radians/degrees

T

stepTincrement in radians/degrees

Conic Graphing allows you to graph a partial conic section. To
do this, you must modify Tmin, Tmax, or Tstep (in parametric
mode) or Tmin, Tmax, or Tstep (in polar mode, for the ellipse and
circle equations 1 and 2 only).

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CONIC ZOOM

The

CONIC ZOOM

settings screen allows you to adjust the viewing
window of the graph quickly. This screen is similar to the
calculator’s zoom settings screen. Zoom settings that do not
apply to conic sections are not displayed.

Zoom Conic

is a new zoom setting that applies only to Conic
Graphing. It changes the viewing window so that you can see the
important characteristics of the conic section, regardless of the
conic section’s position on the graph. The following table
describes how Conic Graphing changes the calculator default
variables, based on the zoom setting you choose.

Note

•

You can only access the CONIC ZOOM screen after you have

selected an equation to graph.

•

You can only access the CONIC ZOOM screen if the mode is

set to MAN.

TI-83 Plus Conic Graphing Page 18

Zoom
Parameter

Description

Zoom Conic

Changes the zoom parameters so that you can see the
important characteristics of the conic section in the
viewing window, regardless of conic section’s position on
the graph. Also, changes the viewing window so that

#X=#

Y, which makes the graph of a circle look like a

circle. (Otherwise, it would look like an ellipse.)
Zoom In

Magnifies the graph around the cursor.
Zoom Out

Views more of the graph around the cursor.
ZBox

Draws a box to define the viewing window.
ZSquare

Changes the viewing window based on the current
window variables so that #X=#Y, which makes the graph
of a circle look like a circle. (Otherwise, it would look like
an ellipse.) The midpoint of the current graph (not the
intersection of the axes) becomes the midpoint of the
new graph.

ZStandard

Sets the standard window variables: Xmin = 110,
Xmax = 10, Ymin = 110, Ymax = 10.

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To see how different zoom settings affect the graph:

1. Make sure that the conic mode is set correctly (to function,

parametric, or polar, depending on what the equation
requires).

2. Select a conic section from the

CONICS

main menu.

3. Select an equation.

4. Enter values for each of the required parameters listed. Use

`

and hto move from one parameter to the next.

Tip

If you enter a value that is invalid for the specific equation, an
error screen displays when you attempt to graph the conic
section.

5. Press

T

.

6. Select

Zoom Conic

and view the graph.

7. Press

T

.

8. Select other zoomsettings to see the differences in the

graph. The graph is displayed after a zoomsetting is
selected (except for zoom settings that require another entry,
such as

Zoom In

or

Zoom Out

).