Quadric Surfaces

The quadric family

Paraboloids and cones

Cross sections and standard form

Cylinders as degenerate quadrics

Cross sections of the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1 parallel to the xy plane are which curves?

The surface x^2/a^2 + y^2/b^2 - z^2/c^2 = 1, with one negative term, is which quadric?

The hyperbolic paraboloid z = x^2/a^2 - y^2/b^2 is commonly called what?

Completing the square on a general quadratic brings a quadric's equation to what?

The hyperboloid of one sheet is used for cooling towers because of which property?

The ellipsoid has three semi-axes a, b, and which third letter? Answer with one lowercase letter.

The cone is the degenerate quadric separating the hyperboloids, its equation equating z squared to a sum. As a two-word name, what is it called? Answer like double cone.

The saddle curves upward along one axis and downward along the other, the landscape of which optimization concept? Answer with one word.

The sphere x^2 + y^2 + z^2 = r^2 is the special case of the ellipsoid with what?

The hyperboloid of two sheets has how many negative squared terms? Answer with a number.