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. 17. x 2 4 + y 2 16 − z 2 = 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. 17. x 2 4 + y 2 16 − z 2 = 4
Solution Summary: The author explains that the given equation is a hyperboloid of one sheet.
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
.2
x + 20x + y + 16y = -20
The equation above defines a circle in the xy-plane.
What are the coordinates of the center of the circle?
A) (-20,–16)
|
B) (-10,–8)
C) (10,8)
D) (20,16)
Identifying surfaces Consider the surfaces defined by thefollowing 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. Sketch the surface.
Chapter 13 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus Enhanced with Graphing Utilities
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