However it is almost circular this graph is

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Unformatted text preview: is almost circular. This graph is exaggerated because we did not change the aspect ratio. You can select Zoom Conic to see an unexaggerated graph of Pluto’s almost circular orbit. 16. Press U to trace the orbit. Note Conic Graphing does not allow for continuous tracing. After you trace the entire orbit, the tracing stops. You can then press the opposite direction arrow key to trace the orbit in the opposite direction. TI-83 Plus Conic Graphing Page 35 Hyperbolas Definition Calculator mode A hyperbola is the set of points in a plane whose distances from two fixed points in the plane have a constant difference. The two fixed points are the foci of the hyperbola. The line through the foci of the hyperbola is the focal axis. The point on the axis halfway between the foci is the hyperbola's center. The points where the focal axis and hyperbola cross are the vertices. Function (X1H) 2 (Y1K) 2 A2 1 B2 = 1 (Y1K) 2 (X1H) 2 =1 A2 1 B 2 X = A sec (T) + H Y = B tan (T) + K Parametric X = B tan (T) + H Y = A sec (T) + K (X13) 2 (Y12) 2 9 1 9 = 1: Vertices (0,2) and (6,2) Polar Focus (-1.243,2) Equations Focus (7.243,2) Focal axis 2ep R = 11e cos (T) 2ep R = 1+e cos (T) 2ep R = 11e sin (T) 2ep R = 1+e sin (T) Center (3,2) TI-83 Plus Conic Graphing Page 36 Example A lamp with an opaque cylindrical shade 1.5 feet in diameter, 2 feet high has a light bulb located at the center of the shade. It casts a shadow, which is of the form of a hyperbola, on a wall 3 feet from the bulb and parallel to the shade. Assume the origin is at the light bulb. Find the vertices, foci, and slope of the asymptotes of the hyperbola. Steps: The equation of the cone of light is 16X 2 16Z 2 2 9 + 9 1 Y = 0. The equation of the wall is: Z = 3. 1. Substitute z into the equation and solve: 16X2 16(3) 2 2 9 + 9 1Y =0 16X2 2 9 1 Y = -16 16X2 Y21 9 = 16 Y2 X2 16 1 9 = 1 TI-83 Plus Conic Graphing Page 37 2. Start the Conic Graphing application. 3. Select HYPERBOLA from the CONICS main menu. 4. Press ] to display the CONIC SETTINGS screen. 5. Select FUNC to change the mode to functional. 6. Select MAN so that you can manually change window settings. 7. Select ESC to return to the HYPERBOLA screen. 8. Select the equation (YK) 2 (XH) 2  =1 A2 B2 9. Enter the values for A, B, H and K. From the solution in step 1, we know that A 2 = 16, B 2 = 9 so that A = 4, B = 3. The problem states that the light bulb is at the origin, so (H,K) is (0,0). TI-83 Plus Conic Graphing Page 38 10. Press e ? to find the center, vertices, foci, and slope of the asymptotes. 11. Press T to change CONIC ZOOM settings. 12. Select Zoom Conic. The graph of the shape of the shadow is drawn. TI-83 Plus Conic Graphing Page 39 Parabolas Definition Calculator mode A set that consists of all the points in a plane equidistant from a given fixed point and a given fixed line in the plane is a parabola. The fixed point is the focus of the parabola. The fixed line is the directrix. The point where the focal axis intersects the parabola is the vertex. Function Parametri...
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This document was uploaded on 12/31/2013.

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