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Y12 2 8 x13 2ep r 11e cos t 2ep r 1e cos t 2ep

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Unformatted text preview: c X = AT2 + H Y=T+K X=T+H Y = AT2 + K Directrix X=1 Vertex (3,2) Polar TI-83 Plus Conic Graphing (Y1K) 2 = 4P(X1H) (X1H) 2 = 4P(Y1K) (Y12) 2 = 8 (X13): Focal axis Equations Focus (5,2) 2ep R = 11e cos (T) 2ep R = 1+e cos (T) 2ep R = 11e sin (T) 2ep R = 1+e sin (T) Page 40 Example Given the equation of projectile motion and necessary values, find the focus and directrix of the path of the projectile (parabola). Assume a ball is thrown with a velocity of 65 ft/sec at an angle of T = tan11 (3/4). Assume that the gravitational force is g = 32 ft/sec 2. Equations of a projectile in motion: X = V 0 cos (T) T 1 Y= V 0 sin (T) T 1 2 GT2 Givens: V 0 = 65 ft/sec G = 32 ft/sec 2 From T = tan11 (3/4): 4 cos (T) = 5 3 sin (T) = 5 TI-83 Plus Conic Graphing Page 41 Steps: 1. Solve for X and Y. 4 X = 65 5 T X = 52T, then X T = 52 , then 3 1 Y = 65 5 T 1 2 32 T2, then Y = 39T 1 16T2 2 X X X Substitute 52 for T: Y = 39 52 1 16 52 2 507 1521 X Y 8 = 1 169 64 Complete the square: 2 2. Start the Conic Graphing application. 3. Select PARABOLA from the CONICS main menu. 4. Press ] to display the CONIC SETTINGS screen. 5. Select PAR to change the mode to parametric. TI-83 Plus Conic Graphing Page 42 6. Select MAN so that you can manually change window settings. 7. Select ESC to return to the PARABOLA screen. 8. Select the equation X = T + H Y = AT 2 + K 9. Enter the values for A, H and K: 1 507 1521 A = / 169 H= 8 K = 64 10. Press T to display the CONIC ZOOM window. 11. Select Zoom Conic. The graph is displayed. 12. Press R to escape from the graph screen. TI-83 Plus Conic Graphing Page 43 13. Press e ? to find the vertex, focus, and directrix. 14. Press S to change the CONIC WINDOW settings. 15. Change the following variables to see the graph from the origin. Xmin = 0 Xmax = 125 Xscl = 5 Ymin = 0 Ymax = 25 Yscl = 5 TI-83 Plus Conic Graphing Page 44 16. Press V to graph the parabola. 17. Press U to trace the trajectory. TI-83 Plus Conic Graphing Page 45 Glossary Term Definition Asymptote A straight line associated with a curve such that as a point moves along an infinite branch of the curve, the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line. Center A point that is related to a geometrical figure in such a way that for any point on the figure there is another point on the figure such that a straight line joining the two points is bisected by the original point. Circle A closed plane curve in a plane whose distance from a given fixed point in the plane is constant. Directrix A straight line the distance to which from any point of a conic section is in fixed ratio to the distance from the same point to a focus. Eccentricity A mathematical constant that for a given conic section is the ratio of the distances from any point of the conic section to a focus and the corresponding directrix. Ellipse A closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant. Focus One of the fixed points that with the cor...
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