Identifying surfaces Consider the surfaces defined by the following equations. a. Identify and briefly describe the surface. b. Find the xy-, xz-, and yz-traces, when they exist. c. Find the intercepts with the three coordinate axes, when they exist. d. Make a sketch of the surface. 16. − x 2 16 + z 2 36 − y 2 25 = 4
Identifying surfaces Consider the surfaces defined by the following equations. a. Identify and briefly describe the surface. b. Find the xy-, xz-, and yz-traces, when they exist. c. Find the intercepts with the three coordinate axes, when they exist. d. Make a sketch of the surface. 16. − x 2 16 + z 2 36 − y 2 25 = 4
Solution Summary: The author explains that the given equation is a hyperboloid of two sheets.
Consider the following equation of a quadric surface.
y²
= z²
X
100 25
+
a. Find the intercepts with the three coordinate axes, if they exist.
b. Find the equations of the xy-, xz-, and yz-traces, if they exist.
c. Identify and sketch a graph of the surface.
A. The surface intersects the x-axis at x = 0.
(Use a comma to separate answers as needed.)
B. There are no x-intercepts.
Find the y-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice.
A. The surface intersects the y-axis at y = 0.
(Use a comma to separate answers as needed.)
B. There are no y-intercepts.
Find the z-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice.
A. The surface intersects the z-axis at z = 0
.
(Use a comma to separate answers as needed.)
B. There are no z-intercepts.
b. Find the equation of the xy-trace, if it exists. Select the correct choice and fill in any answer boxes within your choice.
The trace is not a…
Identify the equation associated with each graphed surface.
(a)
O 2? = - 2² – y? +1
O 22 – 1 = y + x
O 22 +1 = y? + x?
O2? – 1 = y? + x²
O a? + y? = z?
(b)
O a? + y? = z2
O 2? +1 = y? + æ?
O z2 – 1 = y + x
O 2? – 1 = y? + ²
O2? = - 2? – y? + 1
Identify and sketch the graph of the following SURFACES.
2 =
√9 9 - y²
Chapter 13 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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