Brief User Guide for Geometry for the TI-83 Plus and TI-84 Calculators
Content:
Draw triangles, draw a parabola, using the conics App
to draw conics.
INDEX:
To facilitate lookup, the instructions are divided into
the following categories:
I.
Triangles - Draw a triangle, Find lengths of sides of triangle,
II. Parabola - Draw a parabola using the conics App, graph a parabola
using the equation,
III.
Circles - Draw a circle with the Conics Application,
IV. Ellipse - Draw ellipse using Conics App, Draw ellipse using equation,
find tangency point on ellipse, find
definite integral of section of an ellipse,
V. Hyperbola - Draw a hyperbola with the conics application,
IMPORTANT NOTE:
This is a new page. More will be added later.
All of the procedures are not complete.
Those that are not complete will have a notation indicating incompleteness.
RELEASE DATE: Not Released DATE LAST
REVISED: 6/27/09
NOTE: See copy restrictions and printing
hints at the end of this document.
INPORTANT NOTE ON TERMINOLOGY: I will use the terms "draw" and "graph"
with specific meanings.
Draw will mean that the DRAW function of the calculator is being used and graph
will mean that the operation
is being done by the graphing function of the calculator, usually by
plotting an equation.
I. Triangles:
1. Draw a Triangle with Vertices Given:
Let's use the triangle A=(2,1), B= (4,5) , and C=(6,3).
a) Press Y= and clear all entries from the screen and make sure that the
plots are not highlighted. If there
are any drawn sections, erase them by pressing 2ND, DRAW, ENTER to execute
ClrDraw.
b) Press Zoom, 0 (ZoomFit) to get the graphs on
the screen. Now press WINDOW and set
Xmin and Ymin =0.
c) Enter the coordinates so
that you have the following: Line(2,1,6,3). Press ENTER to draw the line.
d) Press 2ND, QUIT, 2ND, ENTRY
to re-display the line command. Edit the command so that you have
The following: Line(6, 3, 4, 5) and press ENTER to draw the line.
e)
Press 2ND,
QUIT, 2ND, ENTRY to re-display the line command. Edit the command so that
you have
The following: Line(2, 1, 4, 5) and press ENTER to draw the line.
Note: Do no use any of the five function keys immediately below the screen
except TRACE or you
may erase the drawings.
2. Find the Lengths of the Sides of a Triangle:
Let's
use the triangle A=(2,1), B= (4,5) , and C=(6,3). We will use the distance
formula √((x_{2}-x_{1})² +(y_{2}-y_{1})²).
a) Find the length
of side AB by entering the following: √((4-2)² +(5-1)²). Press 2ND,
√ for the square root
symbol and the x² key for the exponent. Notice that since the terms are
squared, the order of the x- and
y-terms within the parentheses doesn't matter. It's only important that
the x-terms be together and the
y-terms be together.
b) Press
ENTER and 4.47... will be displayed for the length of side AB.
c) To find
the length of side BC, press 2ND, ENTRY to re-display the above formula and edit
the number
to obtain the following: √((6-4)² +(3-5)²).
d) Press
ENTER and 2.82... will be displayed. (The three dots means there are more
digits displayed that
I did not record.
e) To find
the length of side AC, press 2ND, ENTRY to re-display the above formula and edit
the number
to obtain the following: √((6-2)² +(3-1)²).
f) Press
ENTER and 4.47... will be displayed.
II. Parabola:
1. Draw a Parabola Using the Conics App:
Suppose
that we have a parabola with the following equation: (x-2)² = 8(y+3)
a) Press
APPS, move the cursor to Conics, and press ENTER (or press 0) to display the
comics menu.
b) Press 4 (Parabola); then press
2 for a vertical parabola.
c) Enter 2
for H, -3 for K, 2 for P. Note that P = 8/4 from the equation (x-h)² =
4P(y-k)
d) Press
GRAPH and the parabola will be drawn
Note:
You can use TRACE to move the cursor around the ellipse. You can also use
the Y= key to move
to the
previous screen. The other three keys of that group are disabled.
(More will be added later on this section, II.)
III. Circle:
1. Draw a Circle Using the Conics App:
Suppose
that we have a circle with the following equation: (x-2)²
+(y+3)² =25
a) Press
APPS, move the cursor to Conics, and press ENTER (or press 0) to display the
comics menu.
b) Press 1 (Circle); then press
1 for a circle with the equation of the form we have chosen..
c) Enter 2
for H, -3 for K, and 5 for R. Note that R = √25 form the equation (x-h)²
+(y-k)² =r²
d) Press
GRAPH and the circle will be drawn
Note:
You can use TRACE to move the cursor around the ellipse. You can also use
the Y= key to move
to the
previous screen. The other three keys of that group are disabled.
(More will be added later on this section, III.)
IV. Ellipses:
1. Draw an Ellipse Using the Conics Application:
Suppose that we
have an ellipse with the following equation: (x-2)²/16 +(y+3)²/9 =1
a) Press
APPS, move the cursor to Conics, and press ENTER (or press 0) to display the
comics menu.
b) Press 2
(Ellipse); then press 1 for a horizontal ellipse.
c) Enter 4
for A, 3 for B, 2 for H, and -3 for K.
d) Press
GRAPH and the ellipse will be drawn
Note:
You can use TRACE to move the cursor around the ellipse. You can also use
the Y= key to move
to the
previous screen. The other three keys of that group are disabled.
2. Draw an Ellipse Using the Equation:
First we must
solve the equation, for a horizontal ellipse y=k±√(1-(x-h)²/a² ) for y.
For the ellipse
(x-2)²/16 +(y+3)²/9
=1.That will give us y=-3± 3√((x-2)²/16), which we
will need to enter into Y1 and
Y2.
a) Press Y=
and enter the equation with the plus sign between the number and the square root
sign.
opposite Y1. Notice that the sign before the 3 is a negative sign, (-).
b) Move the
cursor to Y2 and enter the equation with the negative square root term.
Press GRAPH
and the ellipse will be graphed.
c) To get a
better presentation, you may want to set the WINDOW at Xmin=-3, Xmax=8, Ymin=-6,
Ymax=1.
Note about using TRACE: You can use TRACE to move the cursor around on the ellipse, but you
will
need to use the up and down cursor control keys to jump between the top and bottom parts of the
curve.
You
will notice that the trace disappears slightly before you get to x=6 or x=-2,
the vertices. You can
find these values by using TABLE. Set the to find values.
I suggest you first set ΔTbl at 0.1. To do that,
press 2ND, TBLSET and make the change. Press 2ND, TABLE to get back to the
table. You can also
find those "missing" values by pressing 2ND, CALC, ENTER (for Value). and
entering the x-value
for which you want to find y.
3. Find the Value of the Derivative at a Point on the Ellipse.
Let's find the
derivative at x=3
a) First graph
the ellipse as described in number 2 above.
b) From the graph
screen, press2ND, CALC, 6(dy/dx).
c) Press 3, ENTER
and dy/dx= -0.193... will be displayed.
d) If you want to
find the derivative at a point on the bottom half of the ellipse, you must press
the down cursor control arrow. In general, the derivative for the same
x-value will only vary
in sign for the top and bottom portions.
4. Find the Area under the Curve for a Section of the Ellipse.
Let' find the area of
the region between x=2 and x=4.
a) First graph
the ellipse as described in number 2 above.
b) From the graph
screen, press2ND, CALC, 7 ∫f(x)dx. Press the down arrow to move the cursor
to the bottom half of the ellipse.
c) Press 2, ENTER;
then 4, ENTER. ∫f(x)dx= -11.739... will be displayed, and the area from the
x-axis
to the bottom half of the ellipse will be shaded. We must now find the
area above the ellipse and
subtract that value from the 11.739.
d) Press 2ND, DRAW,
ENTER (ClrDraw) to clear the shading from the graph. After the ellipse has
been redrawn, press 2ND, CALC, 7 ∫f(x)dx. Make sure the cursor is on the
top half of the ellipse.
If it isn't, press the up arrow to move the cursor to the top half of the
ellipse.
c) Press 2, ENTER;
then 4, ENTER. ∫f(x)dx=-0.260...will be displayed, and the area from the
x-axis
to the top half of the ellipse will be shaded. We must now find the area
we want by subtracting
the absolute value of the smaller value from the absolute value of the larger
value. That will give
us 11.479 for the final answer.
V. Hyperbola:
1. Draw a Hyperbola Using the Conics Application:
Suppose that we
have a hyperbola with the following equation: (x-2)²/16 - (y+3)²/9
=1
a) Press
APPS, move the cursor to Conics, and press ENTER (or press 0) to display the
comics menu.
b) Press 3
(Hyperbola); then press 1 for a horizontal hyperbola.
c) Enter 4
for A, 3 for B, 2 for H, and -3 for K.
d) Press
GRAPH and the hyperbola will be drawn
Note:
You can use TRACE to move the cursor around the ellipse. You can also use
the Y= key to move
to the
previous screen. The other three keys of that group are disabled.
(More will be added later on this section, V.)
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