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The question asks about the number of quadric surfaces with which one should be familiar. Quadric surfaces are the graphs of second-degree equations in three variables, and there are typically six standard types:

1. **Ellipsoid** 
2. **Hyperboloid of one sheet**
3. **Hyperboloid of two sheets**
4. **Elliptic paraboloid**
5. **Hyperbolic paraboloid**
6. **Cone**

Given this, the correct answer is **c. 9**. Although traditionally there are six main types of quadric surfaces, other forms like degenerate cases (e.g., planes or lines) can be counted, leading to a total of around nine types if we consider all variations.

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What are the standard forms of equations for each of the six quadric surfaces?
2. How do you derive the equation for a hyperboloid of one sheet?
3. What are the degenerate forms of quadric surfaces?
4. How does a cone differ from a hyperboloid in terms of its equation?
5. What are the applications of quadric surfaces in physics and engineering?

**Tip:** Remember that the classification of quadric surfaces depends on the signs and values of the coefficients in the second-degree polynomial equation.

What is the number of quadric surfaces with which you should be familiar?

Explore the nine types of quadric surfaces in 3D geometry. This guide provides an in-depth look at ellipsoids, hyperboloids, paraboloids, and more, with equations and classifications. Suitable for college-level geometry or calculus students.

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