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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 √((x2-x1)² +(y2-y1)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.)

Making it Better:  I would be grateful if you would report any errors or suggestions for improvements to me.  Just click "E-mail Webmaster," site the item number, and tell me your suggested change.

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