E-mail Webmaster _____________ Navigation Home ________________ Recent Additions ________________ English Section Math Tutorials TI Graphing Calculators Mobile Phones & Pads TI Program Descriptions Casio Graphing    Calculator Casio Program Descriptions Casio Programs CFX-9850 & CFX-9750 Brief  Guides CFX-9850 & CFX-9750 User Manual Statistics Guide Casio Programming Keystrokes ________________ Brief Guides Other Calculators HP 43S Calculator Scientific Calculators FAQs for Scientific Calculators =============== Sección Española FAQs en Español FAQs Basicos Mas Dificil Pagina 1 Mas Dificil Pagina 2 Guías en Espaňol TI-82 Espanol TI-82 Estidisticas TI-83 Plus Espanol TI-83 Plus Estidisticas TI-83 Plus Guía Financiera TI-89 Titanium Guía TI-89 Estidisticas TI-89 Guía Financiera   Casio Calculadoras Breve Guía Español Cfx-9850 & Cfx-9750 Casio FAQs en Espanol Calculadoras Científicos FAQs en Espanol ________________ Links Programs at Other Sites Links to Tutorials 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. Printing Hint:  Most browsers will send both the navigation bar and the text to the printer, and, as a result, some printers will cut off the right edge of this document if  the file is printed directly.  To prevent this, you can use landscape, of course.   But if you'd like to get rid of the navigation panel,  highlight the instructions portion only (not the navigation panel) and check "Selection" on the Print dialog box; then click "Apply."  This will eliminate the navigation panel and get all of the instructions on the printed pages.  Some newer printers have a special Web Page function for printing that will print the page without cutting part of it off. Copy Restrictions:  You may make single copies of this document for your own personal use and for the use of other students, but inclusion in another document, publication,  or any use for profit requires my permission.  Teachers may make multiple copies of this document for their students if they first get my permission.  Merely send me an email (Just click on Webmaster in the navigation bar.) with a one-sentence explanation of what you’re using the document for.  I’ll give you permission in a timely manner. 