Parametric Equations Activity

Your job is to come up with the parametric equations for your assigned part of this face. The outline is a circle. The right eye is an ellipse. The left eye is part of a hyperbola. The mouth is part of an ellipse. Put your answer on this activities discussion board. Find a set of paramtric equations that will generate the graph. Let x and y be functions of t. Let t start at 0 and end at 2π. By having everyone use the same values for t, we can graph everyone's results at the same time to build the face. If you find a set of solutions that don't meet the required values of t, go ahead and post what you got, and then you can get some hints about how to adjust your solutions to meet the requirements.

The left eye is part of the top part of a hyperbola with center at (1.5,0.75) and vertex at (1.5,1.25). The x-coordinate goes from 0.5 to 2.5 and the y-coordinates range from 1.25 to about 1.46. The guide box that goes with the left eye has a width of 2 units. You may be asking, "What do you mean by the guide box?" I am talking about that little box that you draw when you are graphing a hyperbola to help you draw a nicer graph. The vertices of the graph touch the box and the asymptotes of the graph go through the corners of the box.

For all parts of the graph right and left are with respect to the face (opposite of your right and left as you look at the face). You may find it helpful to play with the Investigating Parametric Curves applet by David Little.
Bugs Bunny the top of the nose, starting from the bottom point and ending at the y-axis
Daffy Duck the bottom of the nose, starting from bottom point and ending at the y-axis
Elmer Fudd the mouth starting on the right edge and moving to the left (negative x-values to positive x-values)
Foghorn Leghorn the outer part of the right eye
Henery Hawk the iris of the right eye
Marc Anthony the left eyebrow
Marvin the Martianright eyebrow
Pepe Le Pewthe left eye
Petunia Pigthe left half of the face
Porky Pigthe right half of the face

 

The following problem numbers refer to the handout: Conic Section: Parabola in Rectangular, Polar, and Parametric Forms
Roadrunnernumber 2
She Devilnumber 6
Speedy Gonzales number 5
Sylvesternumber 7
Tazmanian Devilnumber 12
Tweety Birdnumber 1
Wile E. Coyote number 3
Yosemite Samnumber 4
Chipnumber 11
Dalenumber 8
Donaldnumber 9

 

Goofy Convert x = 8sin t + 6, y = 4cos t - 3 where 0 ≤ t ≤ 2π to a rectangular equation and identify the type and characteristics of the result.
Mickey Convert x = 4sec t -2, y = 3tan t -3 where 0 ≤ t ≤ 2π to a rectangular equation and identify the type and characteristics of the result.
Minnie Convert to a set of parametric equations and identify the type of conic and vertices and foci of the conic.
Pluto Convert to a set of parametric equations and identify the type of conic and vertices and foci of the conic.