Question 1

Which of the following equations represents an ellipsoid?

Accepted Answer

$$\frac{x^2$}{a^2$} + \frac{y^2$}{b^2$} + \frac{z^2$}{c^2$} = 1$$

Question 2

A surface is defined by $$y = x^2$. What type of surface is this?

Accepted Answer

A parabolic cylinder

Question 3

Which quadric surface has elliptical cross-sections in all three coordinate planes?

Accepted Answer

Ellipsoid

Question 4

The equation $$\frac{x^2$}{a^2$} + \frac{y^2$}{b^2$} = \frac{z}{c}$$ represents which surface?

Accepted Answer

Elliptical paraboloid

Question 5

Which of the following best describes the cross-sections of a hyperbolic paraboloid in planes perpendicular to the $$x-$$axis?

Accepted Answer

Parabolas

Question 6

A surface is given by $$\frac{x^2$}{a^2$} - \frac{y^2$}{b^2$} = \frac{z}{c}. $$What is the name of this surface?

Accepted Answer

Hyperbolic paraboloid

Question 7

Which surface is generated by moving a straight line parallel to the $$z-$$axis along the curve $$y = x^2$ in the xy$-plane?

Accepted Answer

A parabolic cylinder

Question 8

Which of the following equations represents a hyperboloid of one sheet?

Accepted Answer

$$\frac{x^2$}{a^2$} + \frac{y^2$}{b^2$} - \frac{z^2$}{c^2$} = 1$$

Question 9

Which surface has the equation $$\frac{x^2$}{a^2$} - \frac{y^2$}{b^2$} - \frac{z^2$}{c^2$} = 1$$?

Accepted Answer

Hyperboloid of two sheets

Question 10

A real-world application: The shape of a satellite dish is often modeled by which quadric surface?

Accepted Answer

Elliptical paraboloid

Question 11

Which of the following surfaces can be used to model the cooling towers of a power plant?

Accepted Answer

Hyperboloid of one sheet

Question 12

Which surface is described by the equation $$\frac{x^2$}{a^2$} + \frac{y^2$}{b^2$} - \frac{z^2$}{c^2$} = 0$$?

Accepted Answer

Elliptical cone

Question 13

Which of the following best describes the cross-sections of an ellipsoid in the $$xy$$-, $$xz$$-, and $$yz-$$planes?

Accepted Answer

Ellipses

Question 14

A surface is defined by $$x^2$$ + $$y^2$$ = $$r^2. $$What type of surface is this?

Accepted Answer

A circular cylinder

Question 15

Which quadric surface is often used to model the shape of a reflective telescope mirror?

Accepted Answer

Paraboloid

Question 16

Which of the following surfaces has both parabolic and hyperbolic cross-sections?

Accepted Answer

Hyperbolic paraboloid

Question 17

Given the equation $$\frac{x^2$}{a^2$} + \frac{y^2$}{b^2$} = 1$$, what type of surface does this represent in three dimensions?

Accepted Answer

A cylinder

Question 18

Which surface is described by the equation $$z = x^2$ - y^2$?

Accepted Answer

Hyperbolic paraboloid

Question 19

Which of the following surfaces can be used to model the shape of a nuclear reactor containment dome?

Accepted Answer

Ellipsoid

Question 20

Which of the following equations represents a hyperboloid of two sheets?

Accepted Answer

$$-\frac{x^2$}{a^2$} - \frac{y^2$}{b^2$} + \frac{z^2$}{c^2$} = 1$$

Cylinders and Quadric Surfaces

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