In-class work for 8 June 2012
1.) Consider the shape of Pringles:
What quadric surface are individual Pringles?
2.) Reduce the equation to one of the standard forms and classify the surface given by
$$z^2 = 4x^2 + 9y^2 + 36.$$
3.) Reduce the equation to one of the standard forms and classify the surface given by
$$36z^2 = 9x^2 + 4y^2.$$
4.) Reduce the equation to one of the standard forms and classify the surface given by
$$x^2 = y^2 + 250z.$$
5.) Reduce the equation to one of the standard forms and classify the surface given by
$$4z^2 = 25x^2 + 100y^2 - 1.$$
6.) Reduce the equation to one of the standard forms and classify the surface given by
$$2x^2+9y^2 = 18z.$$
7.) Reduce the equation to one of the standard forms and classify the surface given by
$$25x^2 + 100y^2 + 4z^2 = 100.$$
8.) For all equations explored in #2-#7, find traces with the planes $x=k$, $y=k$, and $z=k$ and determine which values of $k$ are legitimate.
9.) Draw the traces found in #8 on their respective coordinate planes and also in 3-dimensional coordinate space.