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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. TI83 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 TI83 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 (Y2) 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. TI83 Plus Conic Graphing Page 31 Steps: 1. Determine the semimajor and semiminor 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
Semimajor axis (which is A) =
Semiminor 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.
TI83 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 = 1e 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.
TI83 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 TI83 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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This document was uploaded on 12/31/2013.
 Fall '13

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