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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. TI83 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) TI83 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 TI83 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). TI83 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. TI83 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.
 Fall '13

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