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83pconicgraphingapp-eng

# Press v to graph the arc you can change the tmin and

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Unformatted text preview: o graph the arc. You can change the Tmin and Tmax values to display the graph of the arcs in different quadrants. TI-83 Plus Conic Graphing Page 29 Ellipses Definition Calculator mode An ellipse is the set of points whose distances from two fixed points in the plane have a constant sum. The two fixed points are the foci of the ellipse. The line through the foci of an ellipse is the ellipse's focal axis. The point on the axis halfway between the foci is the center. The points where the focal axis and ellipse intersect are the ellipse's vertices. Function Parametric X = B cos (T) + H Y = A sin (T) + K Polar Vertex Focus (4.583,2) Vertex Focal axis Center (0,2) Major axis TI-83 Plus Conic Graphing Minor axis (X1H) 2 (Y1K) 2 =1 A2 + B2 2 2 ( X 1 H) (Y1K) B2 + A2 = 1 X = A cos (T) + H Y = B sin (T) + K X 2 (Y-2) 2 = 1: 25 + 4 Focus (-4.583,2) Equations 2ep R = 11e cos (T) 2ep R = 1 + e cos (T) 2ep R = 11e sin (T) 2ep R = 1 + e sin (T) Page 30 Example The planet Pluto moves in an elliptical orbit with the sun at one of the foci. Pluto’s orbit has an aphelion (distance farthest from the sun) of 7304.33 4 10 6 km and a perihelion (distance nearest to the sun) of 4434.99 4 10 6 km (NASA Goddard. 2001). Graph the shape using the polar form. Note To complete this exercise, you need to set your calculator to radian mode before you start the Conic Graphing application. To do this: 1. Press ]. 2. Move the cursor to Radian, and press ¯. 3. Press s to exit the mode screen. TI-83 Plus Conic Graphing Page 31 Steps: 1. Determine the semi-major and semi-minor axes. One astronomical unit = 149.6 4 10 6 km Aphelion = 7304.33 3 149.6 = 48.83 AU Perihelion = 4434.99 3 149.6 = 29.65 AU Semi-major axis (which is A) = Semi-minor axis (which is B): 48.83 + 29.65 = 39.24 2 A 2 − B2 = A 1 29.65, then (39.24)2 − B2 = 39.24 1 29.65. then 1539.776 1 B 2 = (9.59) 2, then B 2 = 1539.776 - (9.59) 2, then B = 1447.8095 = 38.05 2. Determine the eccentricity: (39.24)2 − (38.05)2 A 2 − B2 e= = = .24 A 39.24 3. Determine the distance from the focus to the directrix, or p. B2 p= 3 2 = 75.48 A 2 − B2 4. Start the Conic Graphing application. TI-83 Plus Conic Graphing Page 32 5. Select ELLIPSE from the CONICS main menu. 6. Press ] to display the CONIC SETTINGS screen. 7. Select POL to change the mode to polar. 8. Select MAN so that you can manually change window settings. 9. Select ESC to return to the ELLIPSE screen. 10. Select the equation R = 1e cos (6) 2ep 11. Enter the values for e and p, as defined above in steps 2 and 3. 12. Press e ? to find the center and foci. 13. Press S to change the CONIC WINDOW settings. TI-83 Plus Conic Graphing Page 33 14. Change the following parameters (determined by using the major and minor axis information): 6min = 0 6max = 2S 2S 6step = 32 Xmin = 130 Xmax = 48 Xscl = 5 Ymin = 145 Ymax = 45 Yscl = 5 TI-83 Plus Conic Graphing Page 34 15. Press V to graph the orbit. Pluto’s orbit around the sun is elliptical, as you would expect. However, it...
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